Continuous production of succinic acid from glycerol: A complete experimental and computational study.

In this work, a bioprocess for the fermentation of A. succinogenes for the production of succinic acid from glycerol was developed, employing a continuous bioreactor with recycle. Moreover, a new bioprocess model was constructed, based on an existing double substrate limitation model, which was validated with experimental results for a range of operating parameters. The model was used to successfully predict the dynamics of the continuous fermentation process and was subsequently employed in optimisation studies to compute the optimal conditions, dilution rate, reflux rate and feed glycerol concentration, that maximise the productivity of bio-succinic acid. In addition, a Pareto front for optimal volumetric productivity and glycerol conversion combinations was computed. Maximum volumetric productivity of 0.518 g/L/h, was achieved at the optimal computed conditions, which were experimentally validated. This is the highest bio-succinic acid productivity reported so far, for such a continuous bioprocess.

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy.

In this study, we propose a set of nonlinear differential equations to model the dynamic growth of avascular stage tumors, considering nutrient supply from underlying tissue, innate immune response, contact inhibition of cell migration, and interactions with a chemotherapeutic agent. The model has been validated against available experimental data from the literature for tumor growth. We assume that the size of the modeled tumor is already detectable, and it represents all clinically observed existent cell populations; initial conditions are selected accordingly. Numerical results indicate that the tumor size and regression significantly depend on the strength of the host immune system. The effect of chemotherapy is investigated, not only within the malignancy, but also in terms of the responding immune cells and healthy tissue in the vicinity of a tumor.

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis.

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

A multiscale modelling approach for Haematococcus pluvialis cultivation under different environmental conditions.

Haematococcus pluvialis can produce significant amounts of industrially important compounds belonging to lipids and starch classes, including various specific pigments such as ß-carotene, lutein and astaxanthin, as well as lipids, carbohydrates and proteins. Their production can vary depending on environmental stress conditions like nutrient starvation. However, stress conditions lead also to undesired phenomena such as cell lysis, which is likely to be related to products loss. The microorganism develops towards smaller single cell volumes during the growth process, and eventually, more likely towards lysis when fission (i.e. cell division) slows down. The lysis process takes place simultaneously with nutrient depletion, so both growth and lysis are linked to the change of environmental conditions. In this work, we develop a novel multiscale segregated-structured model based on Population Balance Equations (PBEs) to describe the photoautotrophic growth of H.pluvialis, in particular cell growth, and lysis, making possible the description of the relationship between cell volume/transition, cell loss, and metabolic product availability. Cell volume is the internal coordinate of the population balance model, and its link with intrinsic concentrations is also presented. The model parameters are fitted against experimental data, extensive sensitivity analysis is performed and the model predictive capabilities are tested in terms of cell density distributions, as well as 0th and 1st order moments.

Optimisation of microalgal cultivation via nutrient-enhanced strategies: the biorefinery paradigm.

BACKGROUND: The production of microalgal biofuels, despite their sustainable and renowned potential, is not yet cost-effective compared to current conventional fuel technologies. However, the biorefinery concept increases the prospects of microalgal biomass as an economically viable feedstock suitable for the co-production of multiple biofuels along with value-added chemicals. To integrate biofuels production within the framework of a microalgae biorefinery, it is not only necessary to exploit multi-product platforms, but also to identify optimal microalgal cultivation strategies maximising the microalgal metabolites from which biofuels are obtained: starch and lipids. Whilst nutrient limitation is widely known for increasing starch and lipid formation, this cultivation strategy can greatly reduce microalgal growth. This work presents an optimisation framework combining predictive modelling and experimental methodologies to effectively simulate and predict microalgal growth dynamics and identify optimal cultivation strategies. RESULTS: Microalgal cultivation strategies for maximised starch and lipid formation were successfully established by developing a multi-parametric kinetic model suitable for the prediction of mixotrophic microalgal growth dynamics co-limited by nitrogen and phosphorus. The model's high predictive capacity was experimentally validated against various datasets obtained from laboratory-scale cultures of Chlamydomonas reinhardtii CCAP 11/32C subject to different initial nutrient regimes. The identified model-based optimal cultivation strategies were further validated experimentally and yielded significant increases in starch (+ 270%) and lipid (+ 74%) production against a non-optimised strategy. CONCLUSIONS: The optimised microalgal cultivation scenarios for maximised starch and lipids, as identified by the kinetic model presented here, highlight the benefits of exploiting modelling frameworks as optimisation tools that facilitate the development and commercialisation of microalgae-to-fuel technologies.

Models of microalgal cultivation for added-value products - A review.

Microalgae are considered a promising feedstock for biorefineries given that their chemical composition - rich in carbohydrate and lipid - can be directed towards the co-production of various value-added fuels and chemicals. Production of microalgal biomass for biorefinery purposes requires the identification and establishment of optimal cultivation systems, a crucial yet complicated task due to the numerous factors (e.g. media composition, light, temperature) that simultaneously regulate biomass growth and intracellular composition. Modelling these biological processes, taking into account a single or multiple growth-limiting factors, offers a valuable tool to simulate, design and optimise the dynamics of microalgae cultivation. This review provides an overview of existing models developed to describe microalgal growth processes at the macroscopic scale (also termed black-box models) and discusses their formulation in detail. The black-box kinetic modelling frameworks are compiled into single-factor (6 formulations) and multiple-factor (32 formulations - further divided into non-interactive, additive, and interactive) growth kinetic models, as reported in more than 80 studies, for the prediction of biomass growth as a function of major operational factors such as media composition (e.g. nutrient concentration) and environmental factors (e.g. transient light and temperature). In addition, the review focuses on those models that further account for the production dynamics of two microalgal intracellular products with renowned potential as biorefinery substrates: carbohydrate and lipid molecules. Models of microalgal cultivation dynamics offer a robust engineering tool to understand the natural yet complex responses of microalgae to their growing environment and can help - if used appropriately - to optimise microalgae cultivation and increase the economic viability and sustainability of microalgal systems.

Techno-economic assessment of microbial limonene production.

To satisfy the growing demand for limonene, novel pathways for microbial production of limonene have been sought. A techno-economic analysis is carried out for one such process producing limonene from sugar at an industrial plant scale to assess potential economic viability. A conceptual design of the process is developed, in which a gas stripping-solvent scrubbing method is chosen for recovering limonene from bioreactors based on consideration of payback time and process operability. Minimum limonene selling prices are estimated over a range of fermentation productivity based on the calculation of net present value using discounted cash flow method. Under 45% of the maximum theoretical yield, the selling price reaches $19.9/kg, which could be competitive with established production processes when fermentation productivity is above 0.7 kg/(m3·h). Reduction of cost could be realised through improvement of microbial strains, utilisation of cheaper feedstocks, reduction in capital investment and strategic business planning.

Novel insights into pore-scale dynamics of wettability alteration during low salinity waterflooding.

Low salinity waterflooding has proven to accelerate oil production at core and field scales. Wettability alteration from a more oil-wetting to a more water-wetting condition has been established as one of the most notable effects of low salinity waterflooding. To induce the wettability alteration, low salinity water should be transported to come in contact with the oil-water interfaces. Transport under two-phase flow conditions can be highly influenced by fluids topology that creates connected pathways as well as dead-end regions. It is known that under two-phase flow conditions, the pore space filled by a fluid can be split into flowing (connected pathways) and stagnant (deadend) regions due to fluids topology. Transport in flowing regions is advection controlled and transport in stagnant regions is predominantly diffusion controlled. To understand the full picture of wettability alteration of a rock by injection of low salinity water, it is important to know i) how the injected low salinity water displaces and mixes with the high salinity water, ii) how continuous wettability alteration impacts the redistribution of two immiscible fluids and (ii) role of hydrodynamic transport and mixing between the low salinity water and the formation brine (high salinity water) in wettability alteration. To address these two issues, computational fluid dynamic simulations of coupled dynamic two-phase flow, hydrodynamic transport and wettability alteration in a 2D domain were carried out using the volume of fluid method. The numerical simulations show that when low salinity water was injected, the formation brine (high salinity water) was swept out from the flowing regions by advection. However, the formation brine residing in stagnant regions was diffused very slowly to the low salinity water. The presence of formation brine in stagnant regions created heterogeneous wettability conditions at the pore scale, which led to remarkable two-phase flow dynamics and internal redistribution of oil, which is referred to as the "pull-push" behaviour and has not been addressed before in the literature. Our simulation results imply that the presence of stagnant regions in the tertiary oil recovery impedes the potential of wettability alteration for additional oil recovery. Hence, it would be favorable to inject low salinity water from the beginning of waterflooding to avoid stagnant saturation. We also observed that oil ganglia size was reduced under tertiary mode of low salinity waterflooding compared to the high salinity waterflooding.

Kinetic modelling of starch and lipid formation during mixotrophic, nutrient-limited microalgal growth.

Microalgal starch and lipids, carbon-based storage molecules, are useful as potential biofuel feedstocks. In this work, cultivation strategies maximising starch and lipid formation were established by developing a multi-parameter kinetic model describing microalgal growth as well as starch and lipid formation, in conjunction with laboratory-scale experiments. Growth dynamics are driven by nitrogen-limited mixotrophic conditions, known to increase cellular starch and lipid contents whilst enhancing biomass growth. Model parameters were computed by fitting model outputs to a range of experimental datasets from batch cultures of Chlamydomonas reinhardtii. Predictive capabilities of the model were established against different experimental data. The model was subsequently used to compute optimal nutrient-based cultivation strategies in terms of initial nitrogen and carbon concentrations. Model-based optimal strategies yielded a significant increase of 261% for starch (0.065gCL-1) and 66% for lipid (0.08gCL-1) production compared to base-case conditions (0.018gCL-1 starch, 0.048gCL-1 lipids).

Evaluating feeding strategies for microbial oil production from glycerol by Rhodotorula glutinis.

Oil production, from biodiesel by-product glycerol, through microbial fermentation provides a promising option as part of an integrated biorefinery process. However, bioprocessing improvements are required to make the process more efficient. In the present work, different glycerol feeding strategies were evaluated under fed-batch cultivation of the oleaginous yeast Rhodotorula glutinis. Results showed that the concept of targeting first a cell proliferation stage and then a lipid accumulation stage had beneficial effects on both biomass and oil yields. Continual feeding and pulsed feedings, delivering the same total amount of nutrients, resulted in similar values of cellular biomass (∼25 g/L) and oil content (∼40%). In contrast, continual supply of nutrients at higher rates ( >0.8 g/L/h) led to an increase in both cell densities (30 g/L) and oil content (53%), attaining a high oil yield of 16.28 g/L. This suggests that a continual cultivation with two different rates for each stage constitutes an efficient approach to enhance microbial oil production.

The Influence of Crowding Conditions on the Thermodynamic Feasibility of Metabolic Pathways.

Intracellular reactions are carried out in a crowded medium where the macromolecules occupy ∼40% of the total volume. This decrease in the available volume affects the activity of the reactants. Scaled particle theory is used for the estimation of the activity coefficients of the metabolites, and thereby for the assessment of the impact of the presence of background molecules, on the estimation of the Gibbs free energy change (ΔrG) of the reactions. The lactic acid pathway and the central carbon metabolism of Actinobacillus succinogenes for the production of succinic acid from glycerol have been used as illustrative case studies. Results suggest the importance of maintaining intracellular crowded regions to favor the feasibility of a pathway that in other circumstances would be infeasible. Moreover, the crowding conditions may change the directionality of reactions and can modify the feasible range of fluxes estimated for a metabolic system compared with those obtained at standard biological conditions.

A Lattice-Boltzmann scheme for the simulation of diffusion in intracellular crowded systems.

BACKGROUND: The intracellular environment is a complex and crowded medium where the diffusion of proteins, metabolites and other molecules can be decreased. One of the most popular methodologies for the simulation of diffusion in crowding systems is the Monte Carlo algorithm (MC) which tracks the movement of each particle. This can, however, be computationally expensive for a system comprising a large number of molecules. On the other hand, the Lattice Boltzmann Method (LBM) tracks the movement of collections of molecules, which represents significant savings in computational time. Nevertheless in the classical manifestation of such scheme the crowding conditions are neglected. METHODS: In this paper we use Scaled Particle Theory (SPT) to approximate the probability to find free space for the displacement of hard-disk molecules and in this way to incorporate the crowding effect to the LBM. This new methodology which couples SPT and LBM is validated using a kinetic Monte Carlo (kMC) algorithm, which is used here as our "computational experiment". RESULTS: The results indicate that LBM over-predicts the diffusion in 2D crowded systems, while the proposed coupled SPT-LBM predicts the same behaviour as the kinetic Monte Carlo (kMC) algorithm but with a significantly reduced computational effort. Despite the fact that small deviations between the two methods were observed, in part due to the mesoscopic and microscopic nature of each method, respectively, the agreement was satisfactory both from a qualitative and a quantitative point of view. CONCLUSIONS: A crowding-adaptation to LBM has been developed using SPT, allowing fast simulations of diffusion-systems of different size hard-disk molecules in two-dimensional space. This methodology takes into account crowding conditions; not only the space fraction occupied by the crowder molecules but also the influence of the size of the crowder which can affect the displacement of molecules across the lattice system.

Sampling with poling-based flux balance analysis: optimal versus sub-optimal flux space analysis of Actinobacillus succinogenes.

BACKGROUND: Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value. RESULTS: In this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively "small" characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions. The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol. CONCLUSIONS: A new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO2 must be taken into the system. Solutions involving release of CO2 all give sub-optimal succinic acid production.

Modeling bacterial population growth from stochastic single-cell dynamics.

A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to populations initiated by a larger number of individuals, where the random effects become negligible.

Integrating tracer-based metabolomics data and metabolic fluxes in a linear fashion via Elementary Carbon Modes.

Constraints-based modeling is an emergent area in Systems Biology that includes an increasing set of methods for the analysis of metabolic networks. In order to refine its predictions, the development of novel methods integrating high-throughput experimental data is currently a key challenge in the field. In this paper, we present a novel set of constraints that integrate tracer-based metabolomics data from Isotope Labeling Experiments and metabolic fluxes in a linear fashion. These constraints are based on Elementary Carbon Modes (ECMs), a recently developed concept that generalizes Elementary Flux Modes at the carbon level. To illustrate the effect of our ECMs-based constraints, a Flux Variability Analysis approach was applied to a previously published metabolic network involving the main pathways in the metabolism of glucose. The addition of our ECMs-based constraints substantially reduced the under-determination resulting from a standard application of Flux Variability Analysis, which shows a clear progress over the state of the art. In addition, our approach is adjusted to deal with combinatorial explosion of ECMs in genome-scale metabolic networks. This extension was applied to infer the maximum biosynthetic capacity of non-essential amino acids in human metabolism. Finally, as linearity is the hallmark of our approach, its importance is discussed at a methodological, computational and theoretical level and illustrated with a practical application in the field of Isotope Labeling Experiments.

Modeling flexible pharmacophores with distance geometry, scoring, and bound stretching.

The study of pharmacophores, i.e., of common features between different ligands, is important for the quantitative identification of "compatible" enzymes and binding species. A pharmacophore-based technique is developed that combines multiple conformations with a distance geometry method to create flexible pharmacophore representations. It uses a set of low-energy conformations combined with a new process we call bound stretching to create sets of distance bounds, which contain all or most of the low-energy conformations. The bounds can be obtained using the exact distances between pairs of atoms from the different low-energy conformations. To avoid missing conformations, we can take advantage of the triangle distance inequality between sets of three points to logically expand a set of upper and lower distance bounds (bound stretching). The flexible pharmacophore can be found using a 3-D maximal common subgraph method, which uses the overlap of distance bounds to determine the overlapping structure. A scoring routine is implemented to select the substructures with the largest overlap because there will typically be many overlaps with the maximum number of overlapping bounds. A case study is presented in which 3-D flexible pharmacophores are generated and used to eliminate potential binding species identified by a 2-D pharmacophore method. A second case study creates flexible pharmacophores from a set of thrombin ligands. These are used to compare the new method with existing pharmacophore identification software.

Do elementary flux modes combine linearly at the "atomic" level?: integrating tracer-based metabolomics data and elementary flux modes.

The elementary flux modes (EFMs) approach is an efficient computational tool to predict novel metabolic pathways. Elucidating the physiological relevance of EFMs in a particular cellular state is still an open challenge. Different methods have been presented to carry out this task. However, these methods typically use little experimental data, exploiting methodologies where an a priori optimization function is used to deal with the indetermination underlying metabolic networks. Available "omics" data represent an opportunity to refine current methods. In this article we discuss whether (or not) metabolomics data from isotope labeling experiments (ILEs) and EFMs can be integrated into a linear system of equations. Aside from refining current approaches to infer the physiological relevance of EFMs, this question is important for the integration of metabolomics data from ILEs into metabolic networks, which generally involve non-linear relationships. As a result of our analysis, we concluded that in general the concept of EFMs needs to be redefined at the atomic level for the modeling of ILEs. For this purpose, the concept of Elementary Carbon Modes (ECMs) is introduced.