Systems biology: experimental design

Transfer learning Bayesian optimization for competitor DNA molecule design for use in diagnostic assays

With the rise in engineered biomolecular devices, there is an increased need for tailor-made biological sequences. Often, many similar biological sequences need to be made for a specific application meaning numerous, sometimes prohibitively expensive, lab experiments are necessary for their optimization. This paper presents a transfer learning design of experiments workflow to make this development feasible. By combining a transfer learning surrogate model with Bayesian optimization, we show how the total number of experiments can be reduced by sharing information between optimization tasks. We demonstrate the reduction in the number of experiments using data from the development of DNA competitors for use in an amplification-based diagnostic assay. We use cross-validation to compare the predictive accuracy of different transfer learning models, and then compare the performance of the models for both single objective and penalized optimization tasks.

Mathematical modeling insights into improving CAR T cell therapy for solid tumors with bystander effects

As an adoptive cellular therapy, Chimeric Antigen Receptor T cell (CAR T cell) therapy has shown remarkable success in hematological malignancies but only limited efficacy against solid tumors. Compared with blood cancers, solid tumors present a series of challenges that ultimately combine to neutralize the function of CAR T cells. These challenges include, but are not limited to, antigen heterogeneity - variability in the expression of the antigen on tumor cells, as well as trafficking and infiltration into the solid tumor tissue. A critical question for solving the heterogeneity problem is whether CAR T therapy induces bystander effects, such as antigen spreading. Antigen spreading occurs when CAR T cells activate other endogenous antitumor CD8 T cells against antigens that were not originally targeted. In this work, we develop a mathematical model of CAR T cell therapy for solid tumors that considers both antigen heterogeneity and bystander effects. Our model is based on in vivo treatment data that includes a mixture of target antigen-positive and target antigen-negative tumor cells. We use our model to simulate large cohorts of virtual patients to better understand the relationship involving bystander killing. We also investigate several strategies for enhancing bystander effects, thus increasing CAR T cell therapy's overall efficacy for solid tumors.

Hybrid whale algorithm with evolutionary strategies and filtering for high-dimensional optimization: Application to microarray cancer data

The standard whale algorithm is prone to suboptimal results and inefficiencies in high-dimensional search spaces. Therefore, examining the whale optimization algorithm components is critical. The computer-generated initial populations often exhibit an uneven distribution in the solution space, leading to low diversity. We propose a fusion of this algorithm with a discrete recombinant evolutionary strategy to enhance initialization diversity. We conduct simulation experiments and compare the proposed algorithm with the original WOA on thirteen benchmark test functions. Simulation experiments on unimodal or multimodal benchmarks verified the better performance of the proposed RESHWOA, such as accuracy, minimum mean, and low standard deviation rate. Furthermore, we performed two data reduction techniques, Bhattacharya distance and signal-to-noise ratio. Support Vector Machine (SVM) excels in dealing with high-dimensional datasets and numerical features. When users optimize the parameters, they can significantly improve the SVM's performance, even though it already works well with its default settings. We applied RESHWOA and WOA methods on six microarray cancer datasets to optimize the SVM parameters. The exhaustive examination and detailed results demonstrate that the new structure has addressed WOA's main shortcomings. We conclude that the proposed RESHWOA performed significantly better than the WOA.

Minimally sufficient experimental design using identifiability analysis

Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data.

Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models

Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results.

A Continuation Technique for Maximum Likelihood Estimators in Biological Models

Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical technique to predict the evolution of the MLE as a function of the experimental data. We show that, when considering perturbations from an initial data set, our approach is significantly more computationally efficient that re-fitting model parameters while producing acceptable model fits to the updated data. We use the continuation technique to develop an explicit functional relationship between fit model parameters and experimental data that can be used to measure the sensitivity of the MLE to experimental data. We then leverage this technique to select between model fits with similar information criteria, a priori determine the experimental measurements to which the MLE is most sensitive, and suggest additional experiment measurements that can resolve parameter uncertainty.

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so-called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise

Introduction: Despite continued technological improvements, measurement errors always reduce or distort the information that any real experiment can provide to quantify cellular dynamics. This problem is particularly serious for cell signaling studies to quantify heterogeneity in single-cell gene regulation, where important RNA and protein copy numbers are themselves subject to the inherently random fluctuations of biochemical reactions. Until now, it has not been clear how measurement noise should be managed in addition to other experiment design variables (e.g., sampling size, measurement times, or perturbation levels) to ensure that collected data will provide useful insights on signaling or gene expression mechanisms of interest. Methods: We propose a computational framework that takes explicit consideration of measurement errors to analyze single-cell observations, and we derive Fisher Information Matrix (FIM)-based criteria to quantify the information value of distorted experiments. Results and Discussion: We apply this framework to analyze multiple models in the context of simulated and experimental single-cell data for a reporter gene controlled by an HIV promoter. We show that the proposed approach quantitatively predicts how different types of measurement distortions affect the accuracy and precision of model identification, and we demonstrate that the effects of these distortions can be mitigated through explicit consideration during model inference. We conclude that this reformulation of the FIM could be used effectively to design single-cell experiments to optimally harvest fluctuation information while mitigating the effects of image distortion.

NLoed: A Python Package for Nonlinear Optimal Experimental Design in Systems Biology

Modeling in systems and synthetic biology relies on accurate parameter estimates and predictions. Accurate model calibration relies, in turn, on data and on how well suited the available data are to a particular modeling task. Optimal experimental design (OED) techniques can be used to identify experiments and data collection procedures that will most efficiently contribute to a given modeling objective. However, implementation of OED is limited by currently available software tools that are not well suited for the diversity of nonlinear models and non-normal data commonly encountered in biological research. Moreover, existing OED tools do not make use of the state-of-the-art numerical tools, resulting in inefficient computation. Here, we present the NLoed software package and demonstrate its use with in vivo data from an optogenetic system in Escherichia coli. NLoed is an open-source Python library providing convenient access to OED methods, with particular emphasis on experimental design for systems biology research. NLoed supports a wide variety of nonlinear, multi-input/output, and dynamic models and facilitates modeling and design of experiments over a wide variety of data types. To support OED investigations, the NLoed package implements maximum likelihood fitting and diagnostic tools, providing a comprehensive modeling workflow. NLoed offers an accessible, modular, and flexible OED tool set suited to the wide variety of experimental scenarios encountered in systems biology research. We demonstrate NLoed's capabilities by applying it to experimental design for characterization of a bacterial optogenetic system.

Clinical stratification improves the diagnostic accuracy of small omics datasets within machine learning and genome-scale metabolic modelling methods

BACKGROUND

Recently, multi-omic machine learning architectures have been proposed for the early detection of cancer. However, for rare cancers and their associated small datasets, it is still unclear how to use the available multi-omics data to achieve a mechanistic prediction of cancer onset and progression, due to the limited data available. Hepatoblastoma is the most frequent liver cancer in infancy and childhood, and whose incidence has been lately increasing in several developed countries. Even though some studies have been conducted to understand the causes of its onset and discover potential biomarkers, the role of metabolic rewiring has not been investigated in depth so far.

METHODS

Here, we propose and implement an interpretable multi-omics pipeline that combines mechanistic knowledge from genome-scale metabolic models with machine learning algorithms, and we use it to characterise the underlying mechanisms controlling hepatoblastoma.

RESULTS AND CONCLUSIONS

While the obtained machine learning models generally present a high diagnostic classification accuracy, our results show that the type of omics combinations used as input to the machine learning models strongly affects the detection of important genes, reactions and metabolic pathways linked to hepatoblastoma. Our method also suggests that, in the context of computer-aided diagnosis of cancer, optimal diagnostic accuracy can be achieved by adopting a combination of omics that depends on the patient's clinical characteristics.

Challenges in translational machine learning

Machine learning (ML) algorithms are increasingly being used to help implement clinical decision support systems. In this new field, we define as "translational machine learning", joint efforts and strong communication between data scientists and clinicians help to span the gap between ML and its adoption in the clinic. These collaborations also improve interpretability and trust in translational ML methods and ultimately aim to result in generalizable and reproducible models. To help clinicians and bioinformaticians refine their translational ML pipelines, we review the steps from model building to the use of ML in the clinic. We discuss experimental setup, computational analysis, interpretability and reproducibility, and emphasize the challenges involved. We highly advise collaboration and data sharing between consortia and institutes to build multi-centric cohorts that facilitate ML methodologies that generalize across centers. In the end, we hope that this review provides a way to streamline translational ML and helps to tackle the challenges that come with it.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

Enhancement of Frequency-Specific Hemodynamic Power and Functional Connectivity by Transcranial Photobiomodulation in Healthy Humans

Transcranial photobiomodulation (tPBM) has been considered a safe and effective brain stimulation modality being able to enhance cerebral oxygenation and neurocognitive function. To better understand the underlying neurophysiological effects of tPBM in the human brain, we utilized a 111-channel functional near infrared spectroscopy (fNIRS) system to map cerebral hemodynamic responses over the whole head to 8-min tPBM with 1,064-nm laser given on the forehead of 19 healthy participants. Instead of analyzing broad-frequency hemodynamic signals (0–0.2 Hz), we investigated frequency-specific effects of tPBM on three infra-slow oscillation (ISO) components consisting of endogenic, neurogenic, and myogenic vasomotions. Significant changes induced by tPBM in spectral power of oxygenated hemoglobin concentration (Δ[HbO]), functional connectivity (FC), and global network metrics at each of the three ISO frequency bands were identified and mapped topographically for frequency-specific comparisons. Our novel findings revealed that tPBM significantly increased endogenic Δ[HbO] powers over the right frontopolar area near the stimulation site. Also, we demonstrated that tPBM enabled significant enhancements of endogenic and myogenic FC across cortical regions as well as of several global network metrics. These findings were consistent with recent reports and met the expectation that myogenic oscillation is highly associated with endothelial activity, which is stimulated by tPBM-evoked nitric oxide (NO) release.

Chemometric and sensometric techniques in enological data analysis

Enological evaluations capture the chemical and sensory space of wine using different techniques; many sensory methods as well as a variety of analytical chemistry techniques contribute to the amount of information generated. Data fusion, especially integrating data sets, is important when working with complex systems. The success reported when trying to integrate different modalities is generally low and has been attributed to the lack of statistically considerate strategies focusing on the data handling process. Multiple stages of data handling must be carefully considered when dealing with multi-modal data. In this review, the different stages in the data analysis process were examined. The study revealed misconceptions surrounding the process and elucidated rules for purpose-driven approaches by examining the complexities of each stage and the impact the decisions made at each stage have on the resulting models. The two major modeling approaches are either supervised (discrimination, classification, prediction) or unsupervised (exploration). Supervised approaches were emphatic on the pre-processing steps and prioritized increasing performance. Unsupervised approaches were mostly used for preliminary steps. The review found aspects often neglected when it came to the data collection and capturing which in the end contributed to the low success in combining sensory and chemistry data.

Prediction of Phenolic Contents Based on Ultraviolet-B Radiation in Three-Dimensional Structure of Kale Leaves

Ultraviolet-B (UV-B, 280-315 nm) radiation has been known as an elicitor to enhance bioactive compound contents in plants. However, unpredictable yield is an obstacle to the application of UV-B radiation to controlled environments such as plant factories. A typical three-dimensional (3D) plant structure causes uneven UV-B exposure with leaf position and age-dependent sensitivity to UV-B radiation. The purpose of this study was to develop a model for predicting phenolic accumulation in kale (Brassica oleracea L. var. acephala) according to UV-B radiation interception and growth stage. The plants grown under a plant factory module were exposed to UV-B radiation from UV-B light-emitting diodes with a peak at 310 nm for 6 or 12 h at 23, 30, and 38 days after transplanting. The spatial distribution of UV-B radiation interception in the plants was quantified using ray-tracing simulation with a 3D-scanned plant model. Total phenolic content (TPC), total flavonoid content (TFC), total anthocyanin content (TAC), UV-B absorbing pigment content (UAPC), and the antioxidant capacity were significantly higher in UV-B-exposed leaves. Daily UV-B energy absorbed by leaves and developmental age was used to develop stepwise multiple linear regression models for the TPC, TFC, TAC, and UAPC at each growth stage. The newly developed models accurately predicted the TPC, TFC, TAC, and UAPC in individual leaves with R ² > 0.78 and normalized root mean squared errors of approximately 30% in test data, across the three growth stages. The UV-B energy yields for TPC, TFC, and TAC were the highest in the intermediate leaves, while those for UAPC were the highest in young leaves at the last stage. To the best of our knowledge, this study proposed the first statistical models for estimating UV-B-induced phenolic contents in plant structure. These results provided the fundamental data and models required for the optimization process. This approach can save the experimental time and cost required to optimize the control of UV-B radiation.

A Bayesian Approach to Extracting Kinetic Information from Artificial Enzymatic Networks

In order to create artificial enzymatic networks capable of increasingly complex behavior, an improved methodology in understanding and controlling the kinetics of these networks is needed. Here, we introduce a Bayesian analysis method allowing for the accurate inference of enzyme kinetic parameters and determination of most likely reaction mechanisms, by combining data from different experiments and network topologies in a single probabilistic analysis framework. This Bayesian approach explicitly allows us to continuously improve our parameter estimates and behavior predictions by iteratively adding new data to our models, while automatically taking into account uncertainties introduced by the experimental setups or the chemical processes in general. We demonstrate the potential of this approach by characterizing systems of enzymes compartmentalized in beads inside flow reactors. The methods we introduce here provide a new approach to the design of increasingly complex artificial enzymatic networks, making the design of such networks more efficient, and robust against the accumulation of experimental errors.

Identifying cell-to-cell variability in internalization using flow cytometry

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

Optimal Experimental Design Based on Two-Dimensional Likelihood Profiles

Dynamic behavior of biological systems is commonly represented by non-linear models such as ordinary differential equations. A frequently encountered task in such systems is the estimation of model parameters based on measurement of biochemical compounds. Non-linear models require special techniques to estimate the uncertainty of the obtained model parameters and predictions, e.g. by exploiting the concept of the profile likelihood. Model parameters with significant uncertainty associated with their estimates hinder the interpretation of model results. Informing these model parameters by optimal experimental design minimizes the additional amount of data and therefore resources required in experiments. However, existing techniques of experimental design either require prior parameter distributions in Bayesian approaches or do not adequately deal with the non-linearity of the system in frequentist approaches. For identification of optimal experimental designs, we propose a two-dimensional profile likelihood approach, providing a design criterion which meaningfully represents the expected parameter uncertainty after measuring data for a specified experimental condition. The described approach is implemented into the open source toolbox Data2Dynamics in Matlab. The applicability of the method is demonstrated on an established systems biology model. For this demonstration, available data has been censored to simulate a setting in which parameters are not yet well determined. After determining the optimal experimental condition from the censored ones, a realistic evaluation was possible by re-introducing the censored data point corresponding to the optimal experimental condition. This provided a validation that our method is feasible in real-world applications. The approach applies to, but is not limited to, models in systems biology.

Mathematical Modelling in Plant Synthetic Biology

Mathematical modelling techniques are integral to current research in plant synthetic biology. Modelling approaches can provide mechanistic understanding of a system, allowing predictions of behaviour and thus providing a tool to help design and analyse biological circuits. In this chapter, we provide an overview of mathematical modelling methods and their significance for plant synthetic biology. Starting with the basics of dynamics, we describe the process of constructing a model over both temporal and spatial scales and highlight crucial approaches, such as stochastic modelling and model-based design. Next, we focus on the model parameters and the techniques required in parameter analysis. We then describe the process of selecting a model based on tests and criteria and proceed to methods that allow closer analysis of the system's behaviour. Finally, we highlight the importance of uncertainty in modelling approaches and how to deal with a lack of knowledge, noisy data, and biological variability; all aspects that play a crucial role in the cooperation between the experimental and modelling components. Overall, this chapter aims to illustrate the importance of mathematical modelling in plant synthetic biology, providing an introduction for those researchers who are working with or working on modelling techniques.

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

An experimental-mathematical approach to predict tumor cell growth as a function of glucose availability in breast cancer cell lines

We present the development and validation of a mathematical model that predicts how glucose dynamics influence metabolism and therefore tumor cell growth. Glucose, the starting material for glycolysis, has a fundamental influence on tumor cell growth. We employed time-resolved microscopy to track the temporal change of the number of live and dead tumor cells under different initial glucose concentrations and seeding densities. We then constructed a family of mathematical models (where cell death was accounted for differently in each member of the family) to describe overall tumor cell growth in response to the initial glucose and confluence conditions. The Akaikie Information Criteria was then employed to identify the most parsimonious model. The selected model was then trained on 75% of the data to calibrate the system and identify trends in model parameters as a function of initial glucose concentration and confluence. The calibrated parameters were applied to the remaining 25% of the data to predict the temporal dynamics given the known initial glucose concentration and confluence, and tested against the corresponding experimental measurements. With the selected model, we achieved an accuracy (defined as the fraction of measured data that fell within the 95% confidence intervals of the predicted growth curves) of 77.2 ± 6.3% and 87.2 ± 5.1% for live BT-474 and MDA-MB-231 cells, respectively.

Introducing Parameter Clustering to the OED Procedure for Model Calibration of a Synthetic Inducible Promoter in S. cerevisiae

In recent years, synthetic gene circuits for adding new cell features have become one of the most powerful tools in biological and pharmaceutical research and development. However, because of the inherent non-linearity and noisy experimental data, the experiment-based model calibration of these synthetic parts is perceived as a laborious and time-consuming procedure. Although the optimal experimental design (OED) based on the Fisher information matrix (FIM) has been proved to be an effective means to improve the calibration efficiency, the required calculation increases dramatically with the model size (parameter number). To reduce the OED complexity without losing the calibration accuracy, this paper proposes two OED approaches with different parameter clustering methods and validates the accuracy of calibrated models with in-silico experiments. A model of an inducible synthetic promoter in S. cerevisiae is adopted for bench-marking. The comparison with the traditional off-line OED approach suggests that the OED approaches with both of the clustering methods significantly reduce the complexity of OED problems (for at least 49.0%), while slightly improving the calibration accuracy (11.8% and 19.6% lower estimation error in average for FIM-based and sensitivity-based approaches). This study implicates that for calibrating non-linear models of biological pathways, cluster-based OED could be a beneficial approach to improve the efficiency of optimal experimental design.

Volume of Surgical Freedom: The Most Applicable Anatomical Measurement for Surgical Assessment and 3-Dimensional Modeling

Surgical freedom is the most important metric at the disposal of the surgeon. The volume of surgical freedom (VSF) is a new methodology that produces an optimal qualitative and quantitative representation of an access corridor and provides the surgeon with an anatomical, spatially accurate, and clinically applicable metric. In this study, illustrative dissection examples were completed using two of the most common surgical approaches, the pterional craniotomy and the supraorbital craniotomy. The VSF methodology models the surgical corridor as a cone with an irregular base. The measurement data are fitted to the cone model, and from these fitted data, the volume of the cone is calculated as a volumetric measurement of the surgical corridor. A normalized VSF compensates for inaccurate measurements that may occur as a result of dependence on probe length during data acquisition and provides a fixed reference metric that is applicable across studies. The VSF compensates for multiple inaccuracies in the practical and mathematical methods currently used for quantitative assessment, thereby enabling the production of 3-dimensional models of the surgical corridor. The VSF is therefore an improved standard for assessment of surgical freedom.

Recent advances and future perspectives for automated parameterisation, Bayesian inference and machine learning in voltammetry

Advanced data analysis tools such as mathematical optimisation, Bayesian inference and machine learning have the capability to revolutionise the field of quantitative voltammetry. Nowadays such approaches can be implemented routinely with widely available, user-friendly modern computing languages, algorithms and high speed computing to provide accurate and robust methods for quantitative comparison of experimental data with extensive simulated data sets derived from models proposed to describe complex electrochemical reactions. While the methodology is generic to all forms of dynamic electrochemistry, including the widely used direct current cyclic voltammetry, this review highlights advances achievable in the parameterisation of large amplitude alternating current voltammetry. One significant advantage this technique offers in terms of data analysis is that Fourier transformation provides access to the higher order harmonics that are almost devoid of background current. Perspectives on the technical advances needed to develop intelligent data analysis strategies and make them generally available to users of voltammetry are provided.

Optimal Experimental Design for Systems and Synthetic Biology Using AMIGO2

Dynamic modeling in systems and synthetic biology is still quite a challenge-the complex nature of the interactions results in nonlinear models, which include unknown parameters (or functions). Ideally, time-series data support the estimation of model unknowns through data fitting. Goodness-of-fit measures would lead to the best model among a set of candidates. However, even when state-of-the-art measuring techniques allow for an unprecedented amount of data, not all data suit dynamic modeling.Model-based optimal experimental design (OED) is intended to improve model predictive capabilities. OED can be used to define the set of experiments that would (a) identify the best model or (b) improve the identifiability of unknown parameters. In this chapter, we present a detailed practical procedure to compute optimal experiments using the AMIGO2 toolbox.

Optimally Designed Model Selection for Synthetic Biology

Modeling parts and circuits represents a significant roadblock to automating the Design-Build-Test-Learn cycle in synthetic biology. Once models are developed, discriminating among them requires informative data, computational resources, and skills that might not be readily available. The high cost entailed in model discrimination frequently leads to subjective choices on the selected structures and, in turn, to suboptimal models. Here, we outline frequentist and Bayesian approaches to model discrimination. We ranked three candidate models of a genetic toggle switch, which was adopted as a test case, according to the support from in vivo data. We show that, in each framework, efficient model discrimination can be achieved via optimally designed experiments. We offer a dynamical-systems interpretation of our optimization results and investigate their sensitivity to key parameters in the characterization of synthetic circuits. Our approach suggests that optimal experimental design is an effective strategy to discriminate between competing models of a gene regulatory network. Independent of the adopted framework, optimally designed perturbations exploit regions in the input space that maximally distinguish predictions from the competing models.

Development of new media formulations for cell culture operations based on regression models

The paper discusses modelling and optimization of multi-component cell culture medium. The specific productivity (Qp) was considered a function of the medium components and possible interactions described by linear factors, two-way interactions and squared terms that results in a high dimensional problem where the number of variables p (represented by the medium components and their interactions) is much larger than the number of observations n. Principal Components Regression (PCR), Partial Least Squares (PLS), Lasso and Elastic Net regressions were compared as modelling tools to deal with a high dimensional [Formula: see text] problem. PCR and PLS regression models resulted in better prediction results and were used for robust optimization of the medium composition by a nonlinear optimization. The case studies show that it is possible to formulate new media that result in higher Qp than the ones provided by the initial media experiments available. Also, the multivariate statistical approach permitted us to select media that is most informative about the optimum thus permitting modelling and optimization with a reduced set of initial experiments.

Accelerated knowledge discovery from omics data by optimal experimental design

How to design experiments that accelerate knowledge discovery on complex biological landscapes remains a tantalizing question. We present an optimal experimental design method (coined OPEX) to identify informative omics experiments using machine learning models for both experimental space exploration and model training. OPEX-guided exploration of Escherichia coli’s populations exposed to biocide and antibiotic combinations lead to more accurate predictive models of gene expression with 44% less data. Analysis of the proposed experiments shows that broad exploration of the experimental space followed by fine-tuning emerges as the optimal strategy. Additionally, analysis of the experimental data reveals 29 cases of cross-stress protection and 4 cases of cross-stress vulnerability. Further validation reveals the central role of chaperones, stress response proteins and transport pumps in cross-stress exposure. This work demonstrates how active learning can be used to guide omics data collection for training predictive models, making evidence-driven decisions and accelerating knowledge discovery in life sciences.

How to design experiments that accelerate knowledge discovery on complex biological landscapes remains a tantalizing question. Here, the authors present OPEX, an optimal experimental design method to identify informative omics experiments for both experimental space exploration and model training.

Rapid, precise, and reliable measurement of delay discounting using a Bayesian learning algorithm

Machine learning has the potential to facilitate the development of computational methods that improve the measurement of cognitive and mental functioning. In three populations (college students, patients with a substance use disorder, and Amazon Mechanical Turk workers), we evaluated one such method, Bayesian adaptive design optimization (ADO), in the area of delay discounting by comparing its test-retest reliability, precision, and efficiency with that of a conventional staircase method. In all three populations tested, the results showed that ADO led to 0.95 or higher test-retest reliability of the discounting rate within 10-20 trials (under 1-2 min of testing), captured approximately 10% more variance in test-retest reliability, was 3-5 times more precise, and was 3-8 times more efficient than the staircase method. The ADO methodology provides efficient and precise protocols for measuring individual differences in delay discounting.

Disentangling molecular mechanisms regulating sensitization of interferon alpha signal transduction

Tightly interlinked feedback regulators control the dynamics of intracellular responses elicited by the activation of signal transduction pathways. Interferon alpha (IFNα) orchestrates antiviral responses in hepatocytes, yet mechanisms that define pathway sensitization in response to prestimulation with different IFNα doses remained unresolved. We establish, based on quantitative measurements obtained for the hepatoma cell line Huh7.5, an ordinary differential equation model for IFNα signal transduction that comprises the feedback regulators STAT1, STAT2, IRF9, USP18, SOCS1, SOCS3, and IRF2. The model-based analysis shows that, mediated by the signaling proteins STAT2 and IRF9, prestimulation with a low IFNα dose hypersensitizes the pathway. In contrast, prestimulation with a high dose of IFNα leads to a dose-dependent desensitization, mediated by the negative regulators USP18 and SOCS1 that act at the receptor. The analysis of basal protein abundance in primary human hepatocytes reveals high heterogeneity in patient-specific amounts of STAT1, STAT2, IRF9, and USP18. The mathematical modeling approach shows that the basal amount of USP18 determines patient-specific pathway desensitization, while the abundance of STAT2 predicts the patient-specific IFNα signal response.

Optimal Design of Single-Cell Experiments within Temporally Fluctuating Environments

Modern biological experiments are becoming increasingly complex, and designing these experiments to yield the greatest possible quantitative insight is an open challenge. Increasingly, computational models of complex stochastic biological systems are being used to understand and predict biological behaviors or to infer biological parameters. Such quantitative analyses can also help to improve experiment designs for particular goals, such as to learn more about specific model mechanisms or to reduce prediction errors in certain situations. A classic approach to experiment design is to use the Fisher information matrix (FIM), which quantifies the expected information a particular experiment will reveal about model parameters. The Finite State Projection based FIM (FSP-FIM) was recently developed to compute the FIM for discrete stochastic gene regulatory systems, whose complex response distributions do not satisfy standard assumptions of Gaussian variations. In this work, we develop the FSP-FIM analysis for a stochastic model of stress response genes in S. cerevisae under time-varying MAPK induction. We verify this FSP-FIM analysis and use it to optimize the number of cells that should be quantified at particular times to learn as much as possible about the model parameters. We then extend the FSP-FIM approach to explore how different measurement times or genetic modifications help to minimize uncertainty in the sensing of extracellular environments, and we experimentally validate the FSP-FIM to rank single-cell experiments for their abilities to minimize estimation uncertainty of NaCl concentrations during yeast osmotic shock. This work demonstrates the potential of quantitative models to not only make sense of modern biological data sets, but to close the loop between quantitative modeling and experimental data collection.

Maximum Entropy Framework for Predictive Inference of Cell Population Heterogeneity and Responses in Signaling Networks

Predictive models of signaling networks are essential for understanding cell population heterogeneity and designing rational interventions in disease. However, using computational models to predict heterogeneity of signaling dynamics is often challenging because of the extensive variability of biochemical parameters across cell populations. Here, we describe a maximum entropy-based framework for inference of heterogeneity in dynamics of signaling networks (MERIDIAN). MERIDIAN estimates the joint probability distribution over signaling network parameters that is consistent with experimentally measured cell-to-cell variability of biochemical species. We apply the developed approach to investigate the response heterogeneity in the EGFR/Akt signaling network. Our analysis demonstrates that a significant fraction of cells exhibits high phosphorylated Akt (pAkt) levels hours after EGF stimulation. Our findings also suggest that cells with high EGFR levels predominantly contribute to the subpopulation of cells with high pAkt activity. We also discuss how MERIDIAN can be extended to accommodate various experimental measurements.

A dynamic model linking cell growth to intracellular metabolism and extracellular by-product accumulation

Mathematical modeling of animal cell growth and metabolism is essential for the understanding and improvement of the production of biopharmaceuticals. Models can explain the dynamic behavior of cell growth and product formation, support the identification of the most relevant parameters for process design, and significantly reduce the number of experiments to be performed for process optimization. Few dynamic models have been established that describe both extracellular and intracellular dynamics of growth and metabolism of animal cells. In this study, a model was developed, which comprises a set of 33 ordinary differential equations to describe batch cultivations of suspension AGE1.HN.AAT cells considered for the production of α1-antitrypsin. This model combines a segregated cell growth model with a structured model of intracellular metabolism. Overall, it considers the viable cell concentration, mean cell diameter, viable cell volume, concentration of extracellular substrates, and intracellular concentrations of key metabolites from the central carbon metabolism. Furthermore, the release of metabolic by-products such as lactate and ammonium was estimated directly from the intracellular reactions. Based on the same set of parameters, this model simulates well the dynamics of four independent batch cultivations. Analysis of the simulated intracellular rates revealed at least two distinct cellular physiological states. The first physiological state was characterized by a high glycolytic rate and high lactate production. Whereas the second state was characterized by efficient adenosine triphosphate production, a low glycolytic rate, and reactions of the TCA cycle running in the reverse direction from α-ketoglutarate to citrate. Finally, we show possible applications of the model for cell line engineering and media optimization with two case studies.

Digital Twins and Their Role in Model-Assisted Design of Experiments

Rising demands for biopharmaceuticals and the need to reduce manufacturing costs increase the pressure to develop productive and efficient bioprocesses. Among others, a major hurdle during process development and optimization studies is the huge experimental effort in conventional design of experiments (DoE) methods. As being an explorative approach, DoE requires extensive expert knowledge about the investigated factors and their boundary values and often leads to multiple rounds of time-consuming and costly experiments. The combination of DoE with a virtual representation of the bioprocess, called digital twin, in model-assisted DoE (mDoE) can be used as an alternative to decrease the number of experiments significantly. mDoE enables a knowledge-driven bioprocess development including the definition of a mathematical process model in the early development stages. In this chapter, digital twins and their role in mDoE are discussed. First, statistical DoE methods are introduced as the basis of mDoE. Second, the combination of a mathematical process model and DoE into mDoE is examined. This includes mathematical model structures and a selection scheme for the choice of DoE designs. Finally, the application of mDoE is discussed in a case study for the medium optimization in an antibody-producing Chinese hamster ovary cell culture process.

Effects of antibiotic-free pig rearing on ammonia emissions from five pairs of swine rooms in a wean-to-finish experiment

Antibiotic use and ammonia (NH₃) emissions during animal production are two environmental issues of worldwide concern. However, the role of antibiotics on NH₃ emissions is still unknown. This study evaluated the effects of rearing pigs without antibiotics on NH₃ emissions from a swine experimental building starting with 657 piglets during a wean-to-finish production cycle of 154 days. Pigs were reared in two groups of 10 rooms that were divided into five 2-room pairs (P1-P5) and fed in nine dietary phases. Each pair consisted of one room without antibiotics (no antibiotics in the diet, water, or injectable) and another room as a positive control. Control animals were fed diets containing carbadox-10 (phases 1-4), chlortetracycline (CTC, phase 5), lincomix (phases 6-7), and tylan 40 (phases 8-9). Temperatures in the pig living space and the under-floor manure pit headspace were continuously measured. Ventilation rates at all wall fans and pit fans were obtained by continuous monitoring. Ammonia concentrations in the wall and pit fan exhaust air, and in room inlet air were measured with two multi-gas monitors. Only days that contained at least 18 h of data each day were validated and used. The study generated 1337 room-days of valid data of NH₃ emission rates, with a data completeness of 88.6%. Daily mean NH₃ emission patterns demonstrated large variations between the paired rooms and among different pairs. Within the individual 2-room pairs, no NH₃ emission differences were found in P1 (rooms 1 and 2, p = 0.34) and P2 (rooms 3 and 4, p = 0.44). Significant differences were found in P3-P5 (p < 0.01). The antibiotic-free rooms emitted more NH₃ from P3 and P4, but less NH₃ from P5. However, the combined cycle mean NH₃ emissions from the group of five antibiotic-free rooms and the group of five control rooms were 41.6 ± 10.5 and 39.4 ± 10.6 g d^-1 AU^-1 (mean ± standard deviation. AU = 500 kg live body weight), respectively. Therefore, there was no statistical difference in combined cycle mean NH₃ emissions from rearing pigs with or without antibiotics (p = 0.78). This study also revealed that experiments with multiple replicates and long NH₃ monitoring durations were necessary to avoid potential misinterpretation of experimental results.

CrossPlan: systematic planning of genetic crosses to validate mathematical models

Motivation

Mathematical models of cellular processes can systematically predict the phenotypes of novel combinations of multi-gene mutations. Searching for informative predictions and prioritizing them for experimental validation is challenging since the number of possible combinations grows exponentially in the number of mutations. Moreover, keeping track of the crosses needed to make new mutants and planning sequences of experiments is unmanageable when the experimenter is deluged by hundreds of potentially informative predictions to test.

Results

We present CrossPlan, a novel methodology for systematically planning genetic crosses to make a set of target mutants from a set of source mutants. We base our approach on a generic experimental workflow used in performing genetic crosses in budding yeast. We prove that the CrossPlan problem is NP-complete. We develop an integer-linear-program (ILP) to maximize the number of target mutants that we can make under certain experimental constraints. We apply our method to a comprehensive mathematical model of the protein regulatory network controlling cell division in budding yeast. We also extend our solution to incorporate other experimental conditions such as a delay factor that decides the availability of a mutant and genetic markers to confirm gene deletions. The experimental flow that underlies our work is quite generic and our ILP-based algorithm is easy to modify. Hence, our framework should be relevant in plant and animal systems as well.

Availability and implementation

CrossPlan code is freely available under GNU General Public Licence v3.0 at https://github.com/Murali-group/crossplan.

Supplementary information

Supplementary data are available at Bioinformatics online.

Rethinking the pragmatic systems biology and systems-theoretical biology divide: Toward a complexity-inspired epistemology of systems biomedicine

This paper examines some methodological and epistemological issues underlying the ongoing "artificial" divide between pragmatic-systems biology and systems-theoretical biology. The pragmatic systems view of biology has encountered problems and constraints on its explanatory power because pragmatic systems biologists still tend to view systems as mere collections of parts, not as "emergent realities" produced by adaptive interactions between the constituting components. As such, they are incapable of characterizing the higher-level biological phenomena adequately. The attempts of systems-theoretical biologists to explain these "emergent realities" using mathematics also fail to produce satisfactory results. Given the increasing strategic importance of systems biology, both from theoretical and research perspectives, we suggest that additional epistemological and methodological insights into the possibility of further integration between traditional experimental studies and complex modeling are required. This integration will help to improve the currently underdeveloped pragmatic-systems biology and system-theoretical biology. The "epistemology of complexity," I contend, acts as a glue that connects and integrates different and sometimes opposing viewpoints, perspectives, streams, and practices, thus maintaining intellectual and research coherence of systems research of life. It allows scientists to shift the focus from traditional experimental research to integrated, modeling-based holistic practices capable of providing a comprehensive knowledge of organizing principles of living systems. It also opens the possibility of the development of new practical and theoretical foundations of systems biology to build a better understanding of complex organismic functions.

An easy and efficient approach for testing identifiability

Motivation

The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing this so-called identifiability of model parameters. However, they are typically computationally demanding, difficult to perform and/or not applicable in many application settings.

Results

Here, an approach is presented which enables quickly testing of parameter identifiability. Numerical optimization with a penalty in radial direction enforcing displacement of the parameters is used to check whether estimated parameters are unique, or whether the parameters can be altered without loss of agreement with the data indicating non-identifiability. This Identifiability-Test by Radial Penalization (ITRP) can be employed for every model where optimization-based parameter estimation like least-squares or maximum likelihood is feasible and is therefore applicable for all typical systems biology models. The approach is illustrated and tested using 11 ordinary differential equation (ODE) models.

Availability and implementation

The presented approach can be implemented without great efforts in any modelling framework. It is available within the free Matlab-based modelling toolbox Data2Dynamics. Source code is available at https://github.com/Data2Dynamics.

Contact

ckreutz@fdm.uni-freiburg.de.

Supplementary information

Supplementary data are available at Bioinformatics online.

WASABI: a dynamic iterative framework for gene regulatory network inference

BACKGROUND

Inference of gene regulatory networks from gene expression data has been a long-standing and notoriously difficult task in systems biology. Recently, single-cell transcriptomic data have been massively used for gene regulatory network inference, with both successes and limitations.

RESULTS

In the present work we propose an iterative algorithm called WASABI, dedicated to inferring a causal dynamical network from time-stamped single-cell data, which tackles some of the limitations associated with current approaches. We first introduce the concept of waves, which posits that the information provided by an external stimulus will affect genes one-by-one through a cascade, like waves spreading through a network. This concept allows us to infer the network one gene at a time, after genes have been ordered regarding their time of regulation. We then demonstrate the ability of WASABI to correctly infer small networks, which have been simulated in silico using a mechanistic model consisting of coupled piecewise-deterministic Markov processes for the proper description of gene expression at the single-cell level. We finally apply WASABI on in vitro generated data on an avian model of erythroid differentiation. The structure of the resulting gene regulatory network sheds a new light on the molecular mechanisms controlling this process. In particular, we find no evidence for hub genes and a much more distributed network structure than expected. Interestingly, we find that a majority of genes are under the direct control of the differentiation-inducing stimulus.

CONCLUSIONS

Together, these results demonstrate WASABI versatility and ability to tackle some general gene regulatory networks inference issues. It is our hope that WASABI will prove useful in helping biologists to fully exploit the power of time-stamped single-cell data.

Comparative Assessment of Aspergillosis by Virtual Infection Modeling in Murine and Human Lung

Aspergillus fumigatus is a ubiquitous opportunistic fungal pathogen that can cause severe infections in immunocompromised patients. Conidia that reach the lower respiratory tract are confronted with alveolar macrophages, which are the resident phagocytic cells, constituting the first line of defense. If not efficiently removed in time, A. fumigatus conidia can germinate causing severe infections associated with high mortality rates. Mice are the most extensively used model organism in research on A. fumigatus infections. However, in addition to structural differences in the lung physiology of mice and the human host, applied infection doses in animal experiments are typically orders of magnitude larger compared to the daily inhalation doses of humans. The influence of these factors, which must be taken into account in a quantitative comparison and knowledge transfer from mice to humans, is difficult to measure since in vivo live cell imaging of the infection dynamics under physiological conditions is currently not possible. In the present study, we compare A. fumigatus infection in mice and humans by virtual infection modeling using a hybrid agent-based model that accounts for the respective lung physiology and the impact of a wide range of infection doses on the spatial infection dynamics. Our computer simulations enable comparative quantification of A. fumigatus infection clearance in the two hosts to elucidate (i) the complex interplay between alveolar morphometry and the fungal burden and (ii) the dynamics of infection clearance, which for realistic fungal burdens is found to be more efficiently realized in mice compared to humans.

Component Characterization in a Growth-Dependent Physiological Context: Optimal Experimental Design

Synthetic biology design challenges have driven the use of mathematical models to characterize genetic components and to explore complex design spaces. Traditional approaches to characterization have largely ignored the effect of strain and growth conditions on the dynamics of synthetic genetic circuits, and have thus confounded intrinsic features of the circuit components with cell-level context effects. We present a model that distinguishes an activated gene’s intrinsic kinetics from its physiological context. We then demonstrate an optimal experimental design approach to identify dynamic induction experiments for efficient estimation of the component’s intrinsic parameters. Maximally informative experiments are chosen by formulating the design as an optimal control problem; direct multiple-shooting is used to identify the optimum. Our numerical results suggest that the intrinsic parameters of a genetic component can be more accurately estimated using optimal experimental designs, and that the choice of growth rates, sampling schedule, and input profile each play an important role. The proposed approach to coupled component–host modelling can support gene circuit design across a range of physiological conditions.

The finite state projection based Fisher information matrix approach to estimate information and optimize single-cell experiments

Modern optical imaging experiments not only measure single-cell and single-molecule dynamics with high precision, but they can also perturb the cellular environment in myriad controlled and novel settings. Techniques, such as single-molecule fluorescence in-situ hybridization, microfluidics, and optogenetics, have opened the door to a large number of potential experiments, which begs the question of how to choose the best possible experiment. The Fisher information matrix (FIM) estimates how well potential experiments will constrain model parameters and can be used to design optimal experiments. Here, we introduce the finite state projection (FSP) based FIM, which uses the formalism of the chemical master equation to derive and compute the FIM. The FSP-FIM makes no assumptions about the distribution shapes of single-cell data, and it does not require precise measurements of higher order moments of such distributions. We validate the FSP-FIM against well-known Fisher information results for the simple case of constitutive gene expression. We then use numerical simulations to demonstrate the use of the FSP-FIM to optimize the timing of single-cell experiments with more complex, non-Gaussian fluctuations. We validate optimal simulated experiments determined using the FSP-FIM with Monte-Carlo approaches and contrast these to experiment designs chosen by traditional analyses that assume Gaussian fluctuations or use the central limit theorem. By systematically designing experiments to use all of the measurable fluctuations, our method enables a key step to improve co-design of experiments and quantitative models.

Global optimization using Gaussian processes to estimate biological parameters from image data

Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is typically noisy and non-quantitative. In addition, these models can have a high computational cost, limiting the number of feasible simulations, and therefore rendering most traditional parameter estimation methods unsuitable. In this paper, we present a pipeline that uses Gaussian process learning to estimate biological parameters from noisy, non-quantitative image data when the model has a high computational cost. This approach is first successfully tested on a parametric function with the goal of retrieving the original parameters. We then apply it to estimating parameters in a biological setting by fitting artificial in-situ hybridization (ISH) data of the developing murine limb bud. We expect that this method will be of use in a variety of modeling scenarios where quantitative data is missing and the use of standard parameter estimation approaches in biological modeling is prohibited by the computational cost of the model.

A Pareto approach to resolve the conflict between information gain and experimental costs: Multiple-criteria design of carbon labeling experiments

Science revolves around the best way of conducting an experiment to obtain insightful results. Experiments with maximal information content can be found by computational experimental design (ED) strategies that identify optimal conditions under which to perform the experiment. Several criteria have been proposed to measure the information content, each emphasizing different aspects of the design goal, i.e., reduction of uncertainty. Where experiments are complex or expensive, second sight is at the budget governing the achievable amount of information. In this context, the design objectives cost and information gain are often incommensurable, though dependent. By casting the ED task into a multiple-criteria optimization problem, a set of trade-off designs is derived that approximates the Pareto-frontier which is instrumental for exploring preferable designs. In this work, we present a computational methodology for multiple-criteria ED of information-rich experiments that accounts for virtually any set of design criteria. The methodology is implemented for the case of ¹³C metabolic flux analysis (MFA), which is arguably the most expensive type among the ‘omics’ technologies, featuring dozens of design parameters (tracer composition, analytical platform, measurement selection etc.). Supported by an innovative visualization scheme, we demonstrate with two realistic showcases that the use of multiple criteria reveals deep insights into the conflicting interplay between information carriers and cost factors that are not amendable to single-objective ED. For instance, tandem mass spectrometry turns out as best-in-class with respect to information gain, while it delivers this information quality cheaper than the other, routinely applied analytical technologies. Therewith, our Pareto approach to ED offers the investigator great flexibilities in the conception phase of a study to balance costs and benefits.

Designing experiments is obligatory in the biosciences to valorize their scientific outcome. When the experiments are expensive, unfortunately, in practice often the costs emerge to be showstoppers. In this situation the question arises: How to get the most out of the experiment for your invest in terms of time and money? We approach this question by formulating the design task as a multiple-criteria optimization problem. Its solution produces a set of Pareto-optimal design proposals that feature the trade-off between information gain, as measured by different metrics, and the costs. Then, exploration of the design proposals allows us to make the best decision on information-economic experiments under given circumstances. Implemented in the field of isotope-based metabolic flux analysis, practical application of the Pareto approach provides detailed insight into the tight interplay of plenty of information carriers and cost factors. Supported by an innovative tailored visual representation scheme, the investigator is enabled to explore the options before conducting the experiment. With a practical showcase at hand, our computational study highlights the benefits of incorporating multiple information criteria apart from the costs, balancing the shortcomings of conventional single-objective experimental design strategies.