Dynamic flux balance modeling of S. cerevisiae and E. coli co-cultures for efficient consumption of glucose/xylose mixtures

Current researches into the production of biochemicals from lignocellulosic feedstocks are focused on the identification and engineering of individual microbes that utilize complex sugar mixtures. Microbial consortia represent an alternative approach that has the potential to better exploit individual species capabilities for substrate uptake and biochemical production. In this work, we construct and experimentally validate a dynamic flux balance model of a Saccharomyces cerevisiae and Escherichia coli co-culture designed for efficient aerobic consumption of glucose/xylose mixtures. Each microbe is a substrate specialist, with wild-type S. cerevisiae consuming only glucose and engineered E. coli strain ZSC113 consuming only xylose, to avoid diauxic growth commonly observed in individual microbes. Following experimental identification of a common pH and temperature for optimal co-culture batch growth, we demonstrate that pure culture models developed for optimal growth conditions can be adapted to the suboptimal, common growth condition by adjustment of the non-growth associated ATP maintenance of each microbe. By comparing pure culture model predictions to co-culture experimental data, the inhibitory effect of ethanol produced by S. cerevisiae on E. coli growth was found to be the only interaction necessary to include in the co-culture model to generate accurate batch profile predictions. Co-culture model utility was demonstrated by predicting initial cell concentrations that yield simultaneous glucose and xylose exhaustion for different sugar mixtures. Successful experimental validation of the model predictions demonstrated that steady-state metabolic reconstructions developed for individual microbes can be adapted to develop dynamic flux balance models of microbial consortia for the production of renewable chemicals.     

Kinetic modeling of microbial growth,enzyme activity,and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.     

Mechanistic modeling based process analytical technology implementation for pooling in hydrophobic interaction chromatography

A major challenge in chromatography purification of therapeutic proteins is batch-to-batch variability with respect to impurity levels and product concentration in the feed. Mechanistic model can enable process analytical technology (PAT) implementation by predicting impact of such variations and thereby improving the robustness of the resulting process and controls. This article presents one such application of mechanistic model of hydrophobic interaction chromatography (HIC) as a PAT tool for making robust pooling decisions to enable clearance of aggregates for a monoclonal antibody (mAb) therapeutic. Model predictions were performed before the actual chromatography experiments to facilitate feedforward control. The approach has been successfully demonstrated for four different feeds with varying aggregate levels (3.84%–5.54%) and feed concentration (0.6 mg/mL–1 mg/mL). The resulting pool consistently yielded a product with 1.32 ± 0.03% aggregate vs. a target of 1.5%. A comparison of the traditional approach involving column fractionation with the proposed approach indicates that the proposed approach results in achievement of satisfactory product purity (98.68 ± 0.03% for mechanistic model based PAT controlled pooling vs. 98.64 ± 0.16% for offline column fractionation based pooling). © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 35: e2758, 2019.     

Cross-scale quality assessment of a mechanistic cation exchange chromatography model

Cation exchange chromatography (CEX) is an essential part of most monoclonal antibody (mAb) purification platforms. Process characterization and root cause investigation of chromatographic unit operations are performed using scale down models (SDM). SDM chromatography columns typically have the identical bed height as the respective manufacturing-scale, but a significantly reduced inner diameter. While SDMs enable process development demanding less material and time, their comparability to manufacturing-scale can be affected by variability in feed composition, mobile phase and resin properties, or dispersion effects depending on the chromatography system at hand. Mechanistic models can help to close gaps between scales and reduce experimental efforts compared to experimental SDM applications. In this study, a multicomponent steric mass-action (SMA) adsorption model was applied to the scale-up of a CEX polishing step. Based on chromatograms and elution pool data ranging from laboratory- to manufacturing-scale, the proposed modeling workflow enabled early identification of differences between scales, for example, system dispersion effects or ionic capacity variability. A multistage model qualification approach was introduced to measure the model quality and to understand the model's limitations across scales. The experimental SDM and the in silico model were qualified against large-scale data using the identical state of the art equivalence testing procedure. The mechanistic chromatography model avoided limitations of the SDM by capturing effects of bed height, loading density, feed composition, and mobile phase properties. The results demonstrate the applicability of mechanistic chromatography models as a possible alternative to conventional SDM approaches.     

Bacterial clogging of porous media: A new modelling approach

A comparison is made between existing mathematical models and experimental data that relate the reduction of the saturated hydraulic conductivity (K) of a porous medium to the porosity reduction caused by microbial growth. The models yielded a realistic prediction of a data set obtained with a model porous medium consisting of millimeter‐size glass spheres, but failed to predict the clogging behaviour observed in smaller‐than‐1‐mm sand. A new modelling approach, semi‐mechanistic in nature, is proposed that gives good predictions of fine sand media as well. It relaxes the assumption about uniformly‐thick biofilms by allowing a second arrangement to occur, i.e. discrete plugs filling the pore lumen. The new model requires input data on two intrinsic properties of the system, which renders it sufficiently flexible as to fit very different data sets. The two model parameters are K_min, the minimum K value when all porosity is filled with microorganisms, and B_c, the biovolume fraction at which most cell detachment from biofilm occurs.     

Systematic interpolation method predicts protein chromatographic elution from batch isotherm data without a detailed mechanistic isotherm model

Predicting protein elution for overloaded ion exchange columns requires models capable of describing protein binding over broad ranges of protein and salt concentrations. Although approximate mechanistic models are available, they do not always have the accuracy needed for precise predictions. The aim of this work is to develop a method to predict protein chromatographic behavior from batch isotherm data without relying on a mechanistic model. The method uses a systematic empirical interpolation (EI) scheme coupled with a lumped kinetic model with rate parameters determined from HETP measurements for non‐binding conditions, to numerically predict the column behavior. For two experimental systems considered in this work, predictions based on the EI scheme are in excellent agreement with experimental elution profiles under highly overloaded conditions without using any adjustable parameters. A qualitative study of the sensitivity of predicting protein elution profiles to the precision, granularity, and extent of the batch adsorption data shows that the EI scheme is relatively insensitive to the properties of the dataset used, requiring only that the experimental ranges of protein and salt concentrations overlap those under which the protein actually elutes from the column and possess a ±10% measurement precision.     

Using species distribution models to identify suitable areas for biofuel feedstock production

The 2007 Energy Independence and Security Act mandates a five‐fold increase in US biofuel production by 2022. Given this ambitious policy target, there is a need for spatially explicit estimates of landscape suitability for growing biofuel feedstocks. We developed a suitability modeling approach for two major US biofuel crops, corn (Zea mays) and switchgrass (Panicum virgatum), based upon the use of two presence‐only species distribution models (SDMs): maximum entropy (Maxent) and support vector machines (SVM). SDMs are commonly used for modeling animal and plant distributions in natural environments, but have rarely been used to develop landscape models for cultivated crops. AUC, Kappa, and correlation measures derived from test data indicate that SVM slightly outperformed Maxent in modeling US corn production, although both models produced significantly accurate results. When compared with results from a mechanistic switchgrass model recently developed by Oak Ridge National Laboratory (ORNL), SVM results showed higher correlation than Maxent results with models fit using county‐scale point inputs of switchgrass production derived from expert opinion estimates. However, Maxent results for an alternative switchgrass model developed with point inputs from research trial sites showed higher correlation to the ORNL model than the corresponding results obtained from SVM. Further analysis indicates that both modeling approaches were effective in predicting county‐scale increases in corn production from 2006 to 2007, a time period in which US corn production increased by 24%. We conclude that presence‐only methods are a powerful first‐cut tool for estimating relative land suitability across geographic regions in which candidate biofuel feedstocks can be grown, and may also provide important insight into potential land‐use change patterns likely to be associated with increased biofuel demand.     

Modeling for Understanding v. Modeling for Numbers

I draw a distinction between Modeling for Numbers, which aims to address how much, when, and where questions, and Modeling for Understanding, which aims to address how and why questions. For-numbers models are often empirical, which can be more accurate than their mechanistic analogues as long as they are well calibrated and predictions are made within the domain of the calibration data. To extrapolate beyond the domain of available system-level data, for-numbers models should be mechanistic, relying on the ability to calibrate to the system components even if it is not possible to calibrate to the system itself. However, development of a mechanistic model that is reliable depends on an adequate understanding of the system. This understanding is best advanced using a for-understanding modeling approach. To address how and why questions, for-understanding models have to be mechanistic. The best of these for-understanding models are focused on specific questions, stripped of extraneous detail, and elegantly simple. Once the mechanisms are well understood, one can then decide if the benefits of incorporating the mechanism in a for-numbers model is worth the added complexity and the uncertainty associated with estimating the additional model parameters.     

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.     

MODELS OF CHARACTER DISPLACEMENT AND THE THEORETICAL ROBUSTNESS OF TAXON CYCLES

The appropriateness of the techniques used in modeling character displacement has been the focus of vigorous debate. In this paper, the three competing methods (the coevolutionarily stable community (CSC), the evolutionarily stable strategy (ESS), and quantitative genetic recursion (QGR)) are compared in models using a common ecological setting. Specific predictions of the CSC model have been used to understand features of character displacement among Cnemidophorous lizards on islands off Mexico, Anolis lizards in the Lesser Antilles and Galápagos finches. Nonetheless, the validity of the approach has been repeatedly questioned. Conceptually the three formalisms vary in the degree to which within species variability is allowed in the models. The predictions of the CSC are found not to be robust to even small violation of its fundamental assumption of absolute species monomorphy. We show by simulation and analytical observations that the CSC is not valid under frequency dependent selection, and that the ESS is the limiting case of QGR as intraspecific phenotypic variation goes to zero. Thus the ESS and the QGR models agree closely when the between-phenotype component (BPC) of the niche width is small. However, as the BPC increases, quantitative discrepancies between ESS and QGR predictions increase, although model behavior remains qualitatively similar. A fourth approach, termed “Quantitative Genetic Optimization” (QGO) analysis, is suggested, combining advantages of both the ESS and QGR. Although all approaches support the possibility of taxon cycles, the cycle patterns predicted are qualitatively different and strongly model dependent.     

Spatial scale,topography and thermoregulatory behaviour interact when modelling species’ thermal niches

The spatial scale at which climate and species’ occupancy data are gathered, and the resolution at which ecological models are run, can strongly influence predictions of species performance and distributions. Running model simulations at coarse rather than fine spatial resolutions, for example, can determine if a model accurately predicts the distribution of a species. The impacts of spatial scale on a model's accuracy are particularly pronounced across mountainous terrain. Understanding how these discrepancies arise requires a modelling approach in which the underlying processes that determine a species’ distribution are explicitly described. Here we use a process‐based model to explore how spatial resolution, topography and behaviour alter predictions of a species thermal niche, which in turn constrains its survival and geographic distribution. The model incorporates biophysical equations to predict the operative temperature (T_e), thermal‐dependent performance and survival of a typical insect, with a complex life‐cycle, in its microclimate. We run this model with geographic data from a mountainous terrain in South Africa using climate data at three spatial resolutions. We also explore how behavioural thermoregulation affects predictions of a species performance and survival by allowing the animal to select the optimum thermal location within each coarse‐grid cell. At the regional level, coarse‐resolution models predicted lower T_e at low elevations and higher T_e at high elevations than models run at fine‐resolutions. These differences were more prominent on steep, north‐facing slopes. The discrepancies in T_e in turn affected estimates of the species thermal niche. The modelling framework revealed how spatial resolution and topography influence predictions of species distribution models, including the potential impacts of climate change. These systematic biases must be accounted for when interpreting the outputs of future modelling studies, particularly when species distributions are predicted to shift from uniform to topographically heterogeneous landscapes.     

A Computational Approach to Developing Mathematical Models of Polyploid Meiosis

Mathematical models of meiosis that relate offspring to parental genotypes through parameters such as meiotic recombination frequency have been difficult to develop for polyploids. Existing models have limitations with respect to their analytic potential, their compatibility with insights into mechanistic aspects of meiosis, and their treatment of model parameters in terms of parameter dependencies. In this article I put forward a computational approach to the probabilistic modeling of meiosis. A computer program enumerates all possible paths through the phases of replication, pairing, recombination, and segregation, while keeping track of the probabilities of the paths according to the various parameters involved. Probabilities for classes of genotypes or phenotypes are added, and the resulting formulas are simplified by the symbolic-computation system Mathematica. An example application to autotetraploids results in a model that remedies the limitations of previous models mentioned above. In addition to the immediate implications, the computational approach presented here can be expected to be useful through opening avenues for modeling a host of processes, including meiosis in higher-order ploidies.     

Understanding the mechanism of virus removal by Q sepharose fast flow chromatography during the purification of CHO‐cell derived biotherapeutics

During production of therapeutic monoclonal antibodies (mAbs) in mammalian cell culture, it is important to ensure that viral impurities and potential viral contaminants will be removed during downstream purification. Anion exchange chromatography provides a high degree of virus removal from mAb feedstocks, but the mechanism by which this is achieved has not been characterized. In this work, we have investigated the binding of three viruses to Q sepharose fast flow (QSFF) resin to determine the degree to which electrostatic interactions are responsible for viral clearance by this process. We first used a chromatofocusing technique to determine the isoelectric points of the viruses and established that they are negatively charged under standard QSFF conditions. We then determined that virus removal by this chromatography resin is strongly disrupted by the presence of high salt concentrations or by the absence of the positively charged Q ligand, indicating that binding of the virus to the resin is primarily due to electrostatic forces, and that any non‐electrostatic interactions which may be present are not sufficient to provide virus removal. Finally, we determined the binding profile of a virus in a QSFF column after a viral clearance process. These data indicate that virus particles generally behave similarly to proteins, but they also illustrate the high degree of performance necessary to achieve several logs of virus reduction. Overall, this mechanistic understanding of an important viral clearance process provides the foundation for the development of science‐based process validation strategies to ensure viral safety of biotechnology products. Biotechnol. Bioeng. 2009; 104: 371–380 © 2009 Wiley Periodicals, Inc.     

A mechanistic model for understanding invasions: using the environment as a predictor of population success

Aim We set out to develop a temperature‐ and salinity‐dependent mechanistic population model for copepods that can be used to understand the role of environmental parameters in population growth or decline. Models are an important tool for understanding the dynamics of invasive species; our model can be used to determine an organism’s niche and explore the potential for invasion of a new habitat. Location Strait of Georgia, British Columbia, Canada. Methods We developed a birth rate model to determine the environmental niche for an estuarine copepod. We conducted laboratory experiments to estimate demographic parameters over a range of temperatures and salinities for Eurytemora affinis collected from the Nanaimo Estuary, British Columbia (BC). The parameterized model was then used to explore what environmental conditions resulted in population growth vs. decline. We then re‐parameterized our model using previously published data for E. affinis collected in the Seine Estuary, France (SE), and compared the dynamics of the two populations. Results We established regions in temperature–salinity space where E. affinis populations from BC would likely grow vs. decline. In general, the population from BC exhibited positive and higher intrinsic growth rates at higher temperatures and salinities. The population from SE exhibited positive and higher growth rates with increasing temperature and decreasing salinity. These different relationships with environmental parameters resulted in predictions of complex interactions among temperature, salinity and growth rates if the two subspecies inhabited the same estuary. Main conclusions We developed a new mechanistic model that describes population dynamics in terms of temperature and salinity. This model may prove especially useful in predicting the potential for invasion by copepods transported to Pacific north‐west estuaries via ballast water, or in any system where an ecosystem is subject to invasion by a species that shares demographic characteristics with an established (sub)species.     

Flux balance analysis of primary metabolism in the diatom Phaeodactylum tricornutum

Diatoms (Bacillarophyceae) are photosynthetic unicellular microalgae that have risen to ecological prominence in oceans over the past 30 million years. They are of interest as potential feedstocks for sustainable biofuels. Maximizing production of these feedstocks will require genetic modifications and an understanding of algal metabolism. These processes may benefit from genome‐scale models, which predict intracellular fluxes and theoretical yields, as well as the viability of knockout and knock‐in transformants. Here we present a genome‐scale metabolic model of a fully sequenced and transformable diatom: Phaeodactylum tricornutum. The metabolic network was constructed using the P. tricornutum genome, biochemical literature, and online bioinformatic databases. Intracellular fluxes in P. tricornutum were calculated for autotrophic, mixotrophic and heterotrophic growth conditions, as well as knockout conditions that explore the in silico role of glycolytic enzymes in the mitochondrion. The flux distribution for lower glycolysis in the mitochondrion depended on which transporters for TCA cycle metabolites were included in the model. The growth rate predictions were validated against experimental data obtained using chemostats. Two published studies on this organism were used to validate model predictions for cyclic electron flow under autotrophic conditions, and fluxes through the phosphoketolase, glycine and serine synthesis pathways under mixotrophic conditions. Several gaps in annotation were also identified. The model also explored unusual features of diatom metabolism, such as the presence of lower glycolysis pathways in the mitochondrion, as well as differences between P. tricornutum and other photosynthetic organisms.     

Beyond intuitive modeling: combining biophysical models with innovative experiments to move the circadian clock field forward

Two major approaches have been used to model circadian clocks. Qualitative modeling, used prior to the recent wealth of detailed molecular knowledge, makes general predictions but cannot provide detailed mechanistic insights. The more recent biophysical approach, on the other hand, incorporates the biochemical events that drive the clock and can make detailed and testable molecular predictions. These predictions are being tested using new experimental techniques that measure reaction kinetics and the behavior of individual cells. A joint modeling and experimental approach has recently been used to understand how mutations affecting phosphorylation can lead to a short circadian period in tau mutant hamsters and in humans with familial advanced sleep phase syndrome (FASPS). Another recent study has revealed novel single-cell phenotypes of clock gene mutations, demanding revision of current biophysical models yet validating certain model predictions that were previously overlooked. A new paradigm for clock research is emerging in which modeling inspires new experimental efforts, experimental data inspire new modeling efforts, and joint modeling/experimental studies lead to a deeper understanding of mammalian circadian rhythms.     

Investigation of Design Space for Freeze-Drying: Use of Modeling for Primary Drying Segment of a Freeze-Drying Cycle

In this work, we explore the idea of using mathematical models to build design space for the primary drying portion of freeze-drying process. We start by defining design space for freeze-drying, followed by defining critical quality attributes and critical process parameters. Then using mathematical model, we build an insilico design space. Input parameters to the model (heat transfer coefficient and mass transfer resistance) were obtained from separate experimental runs. Two lyophilization runs are conducted to verify the model predictions. This confirmation of the model predictions with experimental results added to the confidence in the insilico design space. This simple step-by-step approach allowed us to minimize the number of experimental runs (preliminary runs to calculate heat transfer coefficient and mass transfer resistance plus two additional experimental runs to verify model predictions) required to define the design space. The established design space can then be used to understand the influence of critical process parameters on the critical quality attributes for all future cycles.     

A whole-cell computational model predicts phenotype from genotype

Understanding how complex phenotypes arise from individual molecules and their interactions is a primary challenge in biology that computational approaches are poised to tackle. We report a whole-cell computational model of the life cycle of the human pathogen Mycoplasma genitalium that includes all of its molecular components and their interactions. An integrative approach to modeling that combines diverse mathematics enabled the simultaneous inclusion of fundamentally different cellular processes and experimental measurements. Our whole-cell model accounts for all annotated gene functions and was validated against a broad range of data. The model provides insights into many previously unobserved cellular behaviors, including in vivo rates of protein-DNA association and an inverse relationship between the durations of DNA replication initiation and replication. In addition, experimental analysis directed by model predictions identified previously undetected kinetic parameters and biological functions. We conclude that comprehensive whole-cell models can be used to facilitate biological discovery.