Staging of colorectal cancer using lipid biomarkers and machine learning

INTRODUCTION

Colorectal cancer (CRC) is the third most commonly diagnosed cancer worldwide. Alteration in lipid metabolism and chemokine expression are considered hallmark characteristics of malignant progression and metastasis of CRC. Validated diagnostic and prognostic biomarkers are urgently needed to define molecular heterogeneous CRC clinical stages and subtypes, as liver dominant metastasis has poor survival outcomes.

OBJECTIVES

The aim of this study was to integrate lipid changes, concentrations of chemokines, such as platelet factor 4 and interleukin 8, and gene marker status measured in plasma samples, with clinical features from patients at different CRC stages or who had progressed to stage-IV colorectal liver metastasis (CLM).

METHODS

High-resolution liquid chromatography-mass spectrometry (HR-LC-MS) was used to determine the levels of candidate lipid biomarkers in each CRC patient's preoperative plasma samples and combined with chemokine, gene and clinical data. Machine learning models were then trained using known clinical outcomes to select biomarker combinations that best classify CRC stage and group.

RESULTS

Bayesian neural net and multilinear regression-machine learning identified candidate biomarkers that classify CRC (stages I-III), CLM patients and control subjects (cancer-free or patients with polyps/diverticulitis), showing that integrating specific lipid signatures and chemokines (platelet factor-4 and interluken-8; IL-8) can improve prognostic accuracy. Gene marker status could contribute to disease prediction, but requires ubiquitous testing in clinical cohorts.

CONCLUSION

Our findings demonstrate that correlating multiple disease related features with lipid changes could improve CRC prognosis. The identified signatures could be used as reference biomarkers to predict CRC prognosis and classify stages, and monitor therapeutic intervention.

Linear Binary Classifier to Predict Bacterial Biofilm Formation on Polyacrylates

Bacterial infections are increasingly problematic due to the rise of antimicrobial resistance. Consequently, the rational design of materials naturally resistant to biofilm formation is an important strategy for preventing medical device-associated infections. Machine learning (ML) is a powerful method to find useful patterns in complex data from a wide range of fields. Recent reports showed how ML can reveal strong relationships between bacterial adhesion and the physicochemical properties of polyacrylate libraries. These studies used robust and predictive nonlinear regression methods that had better quantitative prediction power than linear models. However, as nonlinear models' feature importance is a local rather than global property, these models were hard to interpret and provided limited insight into the molecular details of material-bacteria interactions. Here, we show that the use of interpretable mass spectral molecular ions and chemoinformatic descriptors and a linear binary classification model of attachment of three common nosocomial pathogens to a library of polyacrylates can provide improved guidance for the design of more effective pathogen-resistant coatings. Relevant features from each model were analyzed and correlated with easily interpretable chemoinformatic descriptors to derive a small set of rules that give model features tangible meaning that elucidate relationships between the structure and function. The results show that the attachment of Pseudomonas aeruginosa and Staphylococcus aureus can be robustly predicted by chemoinformatic descriptors, suggesting that the obtained models can predict the attachment response to polyacrylates to identify anti-attachment materials to synthesize and test in the future.

Systematic Comparison of the Structural and Dynamic Properties of Commonly Used Water Models for Molecular Dynamics Simulations

Water is a unique solvent that is ubiquitous in biology and present in a variety of solutions, mixtures, and materials settings. It therefore forms the basis for all molecular dynamics simulations of biological phenomena, as well as for many chemical, industrial, and materials investigations. Over the years, many water models have been developed, and it remains a challenge to find a single water model that accurately reproduces all experimental properties of water simultaneously. Here, we report a comprehensive comparison of structural and dynamic properties of 30 commonly used 3-point, 4-point, 5-point, and polarizable water models simulated using consistent settings and analysis methods. For the properties of density, coordination number, surface tension, dielectric constant, self-diffusion coefficient, and solvation free energy of methane, models published within the past two decades consistently show better agreement with experimental values compared to models published earlier, albeit with some notable exceptions. However, no single model reproduced all experimental values exactly, highlighting the need to carefully choose a water model for a particular study, depending on the phenomena of interest. Finally, machine learning algorithms quantified the relationship between the water model force field parameters and the resulting bulk properties, providing insight into the parameter-property relationship and illustrating the challenges of developing a water model that can accurately reproduce all properties of water simultaneously.

Machine learning approaches to understand and predict rate constants for organic processes in mixtures containing ionic liquids

The ability to tailor the constituent ions in ionic liquids (ILs) is highly advantageous as it provides access to solvents with a range of physicochemical properties. However, this benefit also leads to large compositional spaces that need to be explored to optimise systems, often involving time consuming experimental work. The use of machine learning methods is an effective way to gain insight based on existing data, to develop structure-property relationships and to allow the prediction of ionic liquid properties. Here we have applied machine learning models to experimentally determined rate constants of a representative organic process (the reaction of pyridine with benzyl bromide) in IL-acetonitrile mixtures. Multiple linear regression (MLREM) and artificial neural networks (BRANNLP) were both able to model the data well. The MLREM model was able to identify the structural features on the cations and anions that had the greatest effect on the rate constant. Secondly, predictive MLREM and BRANNLP models were developed from the full initial set of rate constant data. From these models, a large number of predictions (>9000) of rate constant were made for mixtures of different ionic liquids, at different proportions of ionic liquid and molecular solvent, at different temperatures. A selection of these predictions were tested experimentally, including through the preparation of novel ionic liquids, with overall good agreement between the predicted and experimental data. This study highlights the benefits of using machine learning methods on kinetic data in ionic liquid mixtures to enable the development of rigorous structure-property relationships across multiple variables simultaneously, and to predict properties of new ILs and experimental conditions.

NanoSolveIT Project: Driving nanoinformatics research to develop innovative and integrated tools for in silico nanosafety assessment

Nanotechnology has enabled the discovery of a multitude of novel materials exhibiting unique physicochemical (PChem) properties compared to their bulk analogues. These properties have led to a rapidly increasing range of commercial applications; this, however, may come at a cost, if an association to long-term health and environmental risks is discovered or even just perceived. Many nanomaterials (NMs) have not yet had their potential adverse biological effects fully assessed, due to costs and time constraints associated with the experimental assessment, frequently involving animals. Here, the available NM libraries are analyzed for their suitability for integration with novel nanoinformatics approaches and for the development of NM specific Integrated Approaches to Testing and Assessment (IATA) for human and environmental risk assessment, all within the NanoSolveIT cloud-platform. These established and well-characterized NM libraries (e.g. NanoMILE, NanoSolutions, NANoREG, NanoFASE, caLIBRAte, NanoTEST and the Nanomaterial Registry (>2000 NMs)) contain physicochemical characterization data as well as data for several relevant biological endpoints, assessed in part using harmonized Organisation for Economic Co-operation and Development (OECD) methods and test guidelines. Integration of such extensive NM information sources with the latest nanoinformatics methods will allow NanoSolveIT to model the relationships between NM structure (morphology), properties and their adverse effects and to predict the effects of other NMs for which less data is available. The project specifically addresses the needs of regulatory agencies and industry to effectively and rapidly evaluate the exposure, NM hazard and risk from nanomaterials and nano-enabled products, enabling implementation of computational 'safe-by-design' approaches to facilitate NM commercialization.

Quantitative design rules for protein-resistant surface coatings using machine learning

Preventing biological contamination (biofouling) is key to successful development of novel surface and nanoparticle-based technologies in the manufacturing industry and biomedicine. Protein adsorption is a crucial mediator of the interactions at the bio - nano -materials interface but is not well understood. Although general, empirical rules have been developed to guide the design of protein-resistant surface coatings, they are still largely qualitative. Herein we demonstrate that this knowledge gap can be addressed by using machine learning approaches to extract quantitative relationships between the material surface chemistry and the protein adsorption characteristics. We illustrate how robust linear and non-linear models can be constructed to accurately predict the percentage of protein adsorbed onto these surfaces using lysozyme or fibrinogen as prototype common contaminants. Our computational models could recapitulate the adsorption of proteins on functionalised surfaces in a test set with an r2 of 0.82 and standard error of prediction of 13%. Using the same data set that enabled the development of the Whitesides rules, we discovered an extension to the original rules. We describe a workflow that can be applied to large, consistently obtained data sets covering a broad range of surface functional groups and protein types.

High-Throughput Assessment and Modeling of a Polymer Library Regulating Human Dental Pulp-Derived Stem Cell Behavior

The identification of biomaterials that modulate cell responses is a crucial task for tissue engineering and cell therapy. The identification of novel materials is complicated by the immense number of synthesizable polymers and the time required for testing each material experimentally. In the current study, polymeric biomaterial-cell interactions were assessed rapidly using a microarray format. The attachment, proliferation, and differentiation of human dental pulp stem cells (hDPSCs) were investigated on 141 homopolymers and 400 diverse copolymers. The copolymer of isooctyl acrylate and 2-(methacryloyloxy)ethyl acetoacetate achieved the highest attachment and proliferation of hDPSC, whereas high cell attachment and differentiation of hDPSC were observed on the copolymer of isooctyl acrylate and trimethylolpropane ethoxylate triacrylate. Computational models were generated, relating polymer properties to cellular responses. These models could accurately predict cell behavior for up to 95% of materials within a test set. The models identified several functional groups as being important for supporting specific cell responses. In particular, oxygen-containing chemical moieties, including fragments from the acrylate/acrylamide backbone of the polymers, promoted cell attachment. Small hydrocarbon fragments originating from polymer pendant groups promoted cell proliferation and differentiation. These computational models constitute a key tool to direct the discovery of novel materials within the enormous chemical space available to researchers.

Prediction of Broad-Spectrum Pathogen Attachment to Coating Materials for Biomedical Devices

Bacterial infections in healthcare settings are a frequent accompaniment to both routine procedures such as catheterization and surgical site interventions. Their impact is becoming even more marked as the numbers of medical devices that are used to manage chronic health conditions and improve quality of life increases. The resistance of pathogens to multiple antibiotics is also increasing, adding an additional layer of complexity to the problems of employing safe and effective medical procedures. One approach to reducing the rate of infections associated with implanted and indwelling medical devices is the use of polymers that resist the formation of bacterial biofilms. To significantly accelerate the discovery of such materials, we show how state of the art machine learning methods can generate quantitative predictions for the attachment of multiple pathogens to a large library of polymers in a single model for the first time. Such models facilitate design of polymers with very low pathogen attachment across different bacterial species that will be candidate materials for implantable or indwelling medical devices such as urinary catheters, cochlear implants, and pacemakers.

Demystifying Multitask Deep Neural Networks for Quantitative Structure-Activity Relationships

Deep neural networks (DNNs) are complex computational models that have found great success in many artificial intelligence applications, such as computer vision1,2 and natural language processing.3,4 In the past four years, DNNs have also generated promising results for quantitative structure-activity relationship (QSAR) tasks.5,6 Previous work showed that DNNs can routinely make better predictions than traditional methods, such as random forests, on a diverse collection of QSAR data sets. It was also found that multitask DNN models-those trained on and predicting multiple QSAR properties simultaneously-outperform DNNs trained separately on the individual data sets in many, but not all, tasks. To date there has been no satisfactory explanation of why the QSAR of one task embedded in a multitask DNN can borrow information from other unrelated QSAR tasks. Thus, using multitask DNNs in a way that consistently provides a predictive advantage becomes a challenge. In this work, we explored why multitask DNNs make a difference in predictive performance. Our results show that during prediction a multitask DNN does borrow "signal" from molecules with similar structures in the training sets of the other tasks. However, whether this borrowing leads to better or worse predictive performance depends on whether the activities are correlated. On the basis of this, we have developed a strategy to use multitask DNNs that incorporate prior domain knowledge to select training sets with correlated activities, and we demonstrate its effectiveness on several examples.

Biomimetic molecular design tools that learn, evolve, and adapt

A dominant hallmark of living systems is their ability to adapt to changes in the environment by learning and evolving. Nature does this so superbly that intensive research efforts are now attempting to mimic biological processes. Initially this biomimicry involved developing synthetic methods to generate complex bioactive natural products. Recent work is attempting to understand how molecular machines operate so their principles can be copied, and learning how to employ biomimetic evolution and learning methods to solve complex problems in science, medicine and engineering. Automation, robotics, artificial intelligence, and evolutionary algorithms are now converging to generate what might broadly be called in silico-based adaptive evolution of materials. These methods are being applied to organic chemistry to systematize reactions, create synthesis robots to carry out unit operations, and to devise closed loop flow self-optimizing chemical synthesis systems. Most scientific innovations and technologies pass through the well-known "S curve", with slow beginning, an almost exponential growth in capability, and a stable applications period. Adaptive, evolving, machine learning-based molecular design and optimization methods are approaching the period of very rapid growth and their impact is already being described as potentially disruptive. This paper describes new developments in biomimetic adaptive, evolving, learning computational molecular design methods and their potential impacts in chemistry, engineering, and medicine.

A review of the applications of data mining and machine learning for the prediction of biomedical properties of nanoparticles

This article presents a comprehensive review of applications of data mining and machine learning for the prediction of biomedical properties of nanoparticles of medical interest. The papers reviewed here present the results of research using these techniques to predict the biological fate and properties of a variety of nanoparticles relevant to their biomedical applications. These include the influence of particle physicochemical properties on cellular uptake, cytotoxicity, molecular loading, and molecular release in addition to manufacturing properties like nanoparticle size, and polydispersity. Overall, the results are encouraging and suggest that as more systematic data from nanoparticles becomes available, machine learning and data mining would become a powerful aid in the design of nanoparticles for biomedical applications. There is however the challenge of great heterogeneity in nanoparticles, which will make these discoveries more challenging than for traditional small molecule drug design.

A comprehensive identification-evidence based alternative for HIV/AIDS treatment with HAART in the healthcare industries

BACKGROUND AND OBJECTIVE

The HIV/AIDS-related issue has given rise to a priority concern in which potential new therapies are increasingly highlighted to lessen the negative impact of highly active anti-retroviral therapy (HAART) in the healthcare industry. With the motivation of "medical applications," this study focuses on the main advanced feature selection techniques and classification approaches that reflect a new architecture, and a trial to build a hybrid model for interested parties.

METHODS

This study first uses an integrated linear-nonlinear feature selection technique to identify the determinants influencing HAART medication and utilizes organizations of different condition-attributes to generate a hybrid model based on a rough set classifier to study evolving HIV/AIDS research in order to improve classification performance.

RESULTS

The proposed model makes use of a real data set from Taiwan's specialist medical center. The experimental results show that the proposed model yields a satisfactory result that is superior to the listed methods, and the core condition-attributes PVL, CD4, Code, Age, Year, PLT, and Sex were identified in the HIV/AIDS data set. In addition, the decision rule set created can be referenced as a knowledge-based healthcare service system as the best of evidence-based practices in the workflow of current clinical diagnosis.

CONCLUSIONS

This study highlights the importance of these key factors and provides the rationale that the proposed model is an effective alternative to analyzing sustained HAART medication in follow-up studies of HIV/AIDS treatment in practice.

An Experimental and Computational Approach to the Development of ZnO Nanoparticles that are Safe by Design

Zinc oxide nanoparticles have found wide application due to their unique optoelectronic and photocatalytic characteristics. However, their safety aspects remain of critical concern, prompting the use of physicochemical modifications of pristine ZnO to reduce any potential toxicity. However, the relationships between these modifications and their effects on biology are complex and still relatively unexplored. To address this knowledge gap, a library of 45 types of ZnO nanoparticles with varying particle size, aspect ratio, doping type, doping concentration, and surface coating is synthesized, and their biological effects measured. Three biological assays measuring cell damage or stress are used to study the responses of human umbilical vein endothelial cells (HUVECs) or human hepatocellular liver carcinoma cells (HepG2) to the nanoparticles. These experimental data are used to develop quantitative and predictive computational models linking nanoparticle properties to cell viability, membrane integrity, and oxidative stress. It is found that the concentration of nanoparticles the cells are exposed to, the type of surface coating, the nature and extent of doping, and the aspect ratio of the particles make significant contributions to the cell toxicity of the nanoparticles tested. Our study shows that it is feasible to generate models that could be used to design or optimize nanoparticles with commercially useful properties that are also safe to humans and the environment.

Have artificial neural networks met expectations in drug discovery as implemented in QSAR framework?

INTRODUCTION

Artificial neural networks (ANNs) are highly adaptive nonlinear optimization algorithms that have been applied in many diverse scientific endeavors, ranging from economics, engineering, physics, and chemistry to medical science. Notably, in the past two decades, ANNs have been used widely in the process of drug discovery.

AREAS COVERED

In this review, the authors discuss advantages and disadvantages of ANNs in drug discovery as incorporated into the quantitative structure-activity relationships (QSAR) framework. Furthermore, the authors examine the recent studies, which span over a broad area with various diseases in drug discovery. In addition, the authors attempt to answer the question about the expectations of the ANNs in drug discovery and discuss the trends in this field.

EXPERT OPINION

The old pitfalls of overtraining and interpretability are still present with ANNs. However, despite these pitfalls, the authors believe that ANNs have likely met many of the expectations of researchers and are still considered as excellent tools for nonlinear data modeling in QSAR. It is likely that ANNs will continue to be used in drug development in the future.

Beware of R(2): Simple, Unambiguous Assessment of the Prediction Accuracy of QSAR and QSPR Models

The statistical metrics used to characterize the external predictivity of a model, i.e., how well it predicts the properties of an independent test set, have proliferated over the past decade. This paper clarifies some apparent confusion over the use of the coefficient of determination, R(2), as a measure of model fit and predictive power in QSAR and QSPR modeling. R(2) (or r(2)) has been used in various contexts in the literature in conjunction with training and test data for both ordinary linear regression and regression through the origin as well as with linear and nonlinear regression models. We analyze the widely adopted model fit criteria suggested by Golbraikh and Tropsha ( J. Mol. Graphics Modell. 2002 , 20 , 269 - 276 ) in a strict statistical manner. Shortcomings in these criteria are identified, and a clearer and simpler alternative method to characterize model predictivity is provided. The intent is not to repeat the well-documented arguments for model validation using test data but rather to guide the application of R(2) as a model fit statistic. Examples are used to illustrate both correct and incorrect uses of R(2). Reporting the root-mean-square error or equivalent measures of dispersion, which are typically of more practical importance than R(2), is also encouraged, and important challenges in addressing the needs of different categories of users such as computational chemists, experimental scientists, and regulatory decision support specialists are outlined.

Sparse feature selection methods identify unexpected global cellular response to strontium-containing materials

Despite the increasing sophistication of biomaterials design and functional characterization studies, little is known regarding cells' global response to biomaterials. Here, we combined nontargeted holistic biological and physical science techniques to evaluate how simple strontium ion incorporation within the well-described biomaterial 45S5 bioactive glass (BG) influences the global response of human mesenchymal stem cells. Our objective analyses of whole gene-expression profiles, confirmed by standard molecular biology techniques, revealed that strontium-substituted BG up-regulated the isoprenoid pathway, suggesting an influence on both sterol metabolite synthesis and protein prenylation processes. This up-regulation was accompanied by increases in cellular and membrane cholesterol and lipid raft contents as determined by Raman spectroscopy mapping and total internal reflection fluorescence microscopy analyses and by an increase in cellular content of phosphorylated myosin II light chain. Our unexpected findings of this strong metabolic pathway regulation as a response to biomaterial composition highlight the benefits of discovery-driven nonreductionist approaches to gain a deeper understanding of global cell-material interactions and suggest alternative research routes for evaluating biomaterials to improve their design.

Sparse feature selection identifies H2A.Z as a novel, pattern-specific biomarker for asymmetrically self-renewing distributed stem cells

There is a long-standing unmet clinical need for biomarkers with high specificity for distributed stem cells (DSCs) in tissues, or for use in diagnostic and therapeutic cell preparations (e.g., bone marrow). Although DSCs are essential for tissue maintenance and repair, accurate determination of their numbers for medical applications has been problematic. Previous searches for biomarkers expressed specifically in DSCs were hampered by difficulty obtaining pure DSCs and by the challenges in mining complex molecular expression data. To identify such useful and specific DSC biomarkers, we combined a novel sparse feature selection method with combinatorial molecular expression data focused on asymmetric self-renewal, a conspicuous property of DSCs. The analysis identified reduced expression of the histone H2A variant H2A.Z as a superior molecular discriminator for DSC asymmetric self-renewal. Subsequent molecular expression studies showed H2A.Z to be a novel "pattern-specific biomarker" for asymmetrically self-renewing cells, with sufficient specificity to count asymmetrically self-renewing DSCs in vitro and potentially in situ.

Multivariate statistical analysis methods in QSAR

The emphasis of this review is particularly on multivariate statistical methods currently used in quantitative structure–activity relationship (QSAR) studies.

Towards computational design of zeolite catalysts for CO2 reduction

Computational search of structure database for CO₂ reduction catalysts using molecular simulation and machine learning.

Modelling and predicting the biological effects of nanomaterials

The commercial applications of nanoparticles are growing rapidly, but we know relatively little about how nanoparticles interact with biological systems. Their value--but also their risk--is related to their nanophase properties being markedly different to those of the same material in bulk. Experiments to determine how nanoparticles are taken up, distributed, modified, and elicit any adverse effects are essential. However, cost and time considerations mean that predictive models would also be extremely valuable, particularly assisting regulators to minimize health and environmental risks. We used novel sparse machine learning methods that employ Bayesian neural networks to model three nanoparticle data sets using both linear and nonlinear machine learning methods. The first data comprised iron oxide nanoparticles decorated with 108 different molecules tested against five cell lines, HUVEC, pancreatic cancer, and three macrophage or macrophage-like lines. The second data set comprised 52 nanoparticles with various core compositions, coatings, and surface attachments. The nanoparticles were characterized using four descriptors (size, relaxivities, and zeta potential), and their biological effects on four cells lines assessed using four biological assays per cell line and four concentrations per assay. The third data set involved the biological responses to gold nanoparticles functionalized by 80 different small molecules. Nonspecific binding and binding to AChE were the biological endpoints modelled. The biological effects of nanoparticles were modelled using molecular descriptors for the molecules that decorated the nanoparticle surface. Models with good statistical quality were constructed for most biological endpoints. These proof-of-concept models show that modelling biological effects of nanomaterials is possible using modern modelling methods.

Capturing the crystal: prediction of enthalpy of sublimation, crystal lattice energy, and melting points of organic compounds

Accurate computational prediction of melting points and aqueous solubilities of organic compounds would be very useful but is notoriously difficult. Predicting the lattice energies of compounds is key to understanding and predicting their melting behavior and ultimately their solubility behavior. We report robust, predictive, quantitative structure-property relationship (QSPR) models for enthalpies of sublimation, crystal lattice energies, and melting points for a very large and structurally diverse set of small organic compounds. Sparse Bayesian feature selection and machine learning methods were employed to select the most relevant molecular descriptors for the model and to generate parsimonious quantitative models. The final enthalpy of sublimation model is a four-parameter multilinear equation that has an r(2) value of 0.96 and an average absolute error of 7.9 ± 0.3 kJ.mol(-1). The melting point model can predict this property with a standard error of 45° ± 1 K and r(2) value of 0.79. Given the size and diversity of the training data, these conceptually transparent and accurate models can be used to predict sublimation enthalpy, lattice energy, and melting points of organic compounds in general.

Modeling biological activities of nanoparticles

Products are increasingly incorporating nanomaterials, but we have a poor understanding of their adverse effects. To assess risk, regulatory authorities need more experimental testing of nanoparticles. Computational models play a complementary role in allowing rapid prediction of potential toxicities of new and modified nanomaterials. We generated quantitative, predictive models of cellular uptake and apoptosis induced by nanoparticles for several cell types. We illustrate the potential of computational methods to make a contribution to nanosafety.

Modelling human embryoid body cell adhesion to a combinatorial library of polymer surfaces

Designing materials to control biology is an intense focus of biomaterials and regenerative medicine research. Discovering and designing materials with appropriate biological compatibility or active control of cells and tissues is being increasingly undertaken using high throughput synthesis and assessment methods. We report a relatively simple but powerful machine-learning method of generating models that link microscopic or molecular properties of polymers or other materials to their biological effects. We illustrate the potential of these methods by developing the first robust, predictive, quantitative, and purely computational models of adhesion of human embryonic stem cell embryoid bodies (hEB) to the surfaces of a 496-member polymer micro array library.

Robust, quantitative tools for modelling ex-vivo expansion of haematopoietic stem cells and progenitors

Despite substantial research activity on bioreactor design and experiments, there are very few reports of modelling tools that can be used to generate predictive models describing how bioreactor parameters affect performance. New developments in mathematics, such as sparse Bayesian feature selection methods and nonlinear model-free modelling regression methods, offer considerable promise for modelling diverse types of data. The utility of these mathematical tools in stem cell biology are demonstrated by analysis of a large set of bioreactor data derived from the literature. In spite of the diversity of the data sources, and the inherent difficulty in representing bioreactor variables, these modelling methods were able to develop robust, quantitative, predictive models. These models relate bioreactor operational parameters to the degree of expansion of haematopoietic stem cells or their progenitors, and also identify the bioreactor variables that are most likely to affect performance across many experiments. These methods show substantial promise in assisting the design and optimisation of stem cell bioreactors.