Benchmarking optimization methods for parameter estimation in large kinetic models

Multi-cell-line learning for the data-driven construction of mechanistic metabolic models

Mammalian cells are commonly used as hosts in cell culture for biologics production in the pharmaceutical industry. Structured mechanistic models of metabolism have been used to capture complex cellular mechanisms that contribute to varying metabolic shifts in different cell lines. However, little research has focused on the impact of temporal changes in enzyme abundance and activity on the modeling of cell metabolism. In this work, we present a framework for constructing mechanistic models of metabolism that integrate growth-signaling control of enzyme activity and transcript dynamics. The proposed approach is applied to build models for three Chinese hamster ovary (CHO) cell lines using fed-batch culture data and time-series transcript profiles. Leveraging information from the transcriptome data, we develop a parameter estimation approach based on multi-cell-line (MCL) learning, which combines data sets from different cell lines and trains the individual cell-line models jointly to improve model accuracy. The computational results demonstrate the important role of growth signaling and transcript variability in metabolic models as well as the virtue of the MCL approach for constructing cell-line models with a limited amount of data. The resulting models exhibit a high level of accuracy in predicting distinct metabolic behaviors in the different cell lines; these models can potentially be used to accelerate the process and cell-line development for the biomanufacturing of new protein therapeutics.

Microbiome modeling: a beginner's guide

Microbiomes, comprised of diverse microbial species and viruses, play pivotal roles in human health, environmental processes, and biotechnological applications and interact with each other, their environment, and hosts via ecological interactions. Our understanding of microbiomes is still limited and hampered by their complexity. A concept improving this understanding is systems biology, which focuses on the holistic description of biological systems utilizing experimental and computational methods. An important set of such experimental methods are metaomics methods which analyze microbiomes and output lists of molecular features. These lists of data are integrated, interpreted, and compiled into computational microbiome models, to predict, optimize, and control microbiome behavior. There exists a gap in understanding between microbiologists and modelers/bioinformaticians, stemming from a lack of interdisciplinary knowledge. This knowledge gap hinders the establishment of computational models in microbiome analysis. This review aims to bridge this gap and is tailored for microbiologists, researchers new to microbiome modeling, and bioinformaticians. To achieve this goal, it provides an interdisciplinary overview of microbiome modeling, starting with fundamental knowledge of microbiomes, metaomics methods, common modeling formalisms, and how models facilitate microbiome control. It concludes with guidelines and repositories for modeling. Each section provides entry-level information, example applications, and important references, serving as a valuable resource for comprehending and navigating the complex landscape of microbiome research and modeling.

Cell-specific models of hiPSC-CMs developed by the gradient-based parameter optimization method fitting two different action potential waveforms

Parameter optimization (PO) methods to determine the ionic current composition of experimental cardiac action potential (AP) waveform have been developed using a computer model of cardiac membrane excitation. However, it was suggested that fitting a single AP record in the PO method was not always successful in providing a unique answer because of a shortage of information. We found that the PO method worked perfectly if the PO method was applied to a pair of a control AP and a model output AP in which a single ionic current out of six current species, such as IKr, ICaL, INa, IKs, IKur or IbNSC was partially blocked in silico. When the target was replaced by a pair of experimental control and IKr-blocked records of APs generated spontaneously in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), the simultaneous fitting of the two waveforms by the PO method was hampered to some extent by the irregular slow fluctuations in the Vm recording and/or sporadic alteration in AP configurations in the hiPSC-CMs. This technical problem was largely removed by selecting stable segments of the records for the PO method. Moreover, the PO method was made fail-proof by running iteratively in identifying the optimized parameter set to reconstruct both the control and the IKr-blocked AP waveforms. In the lead potential analysis, the quantitative ionic mechanisms deduced from the optimized parameter set were totally consistent with the qualitative view of ionic mechanisms of AP so far described in physiological literature.

Identifying Key Regulatory Genes in Drug Resistance Acquisition: Modeling Pseudotime Trajectories of Breast Cancer Single-Cell Transcriptome

Single-cell RNA-sequencing (scRNA-seq) technology has provided significant insights into cancer drug resistance at the single-cell level. However, understanding dynamic cell transitions at the molecular systems level remains limited, requiring a systems biology approach. We present an approach that combines mathematical modeling with a pseudotime analysis using time-series scRNA-seq data obtained from the breast cancer cell line MCF-7 treated with tamoxifen. Our single-cell analysis identified five distinct subpopulations, including tamoxifen-sensitive and -resistant groups. Using a single-gene mathematical model, we discovered approximately 560-680 genes out of 6000 exhibiting multistable expression states in each subpopulation, including key estrogen-receptor-positive breast cancer cell survival genes, such as RPS6KB1. A bifurcation analysis elucidated their regulatory mechanisms, and we mapped these genes into a molecular network associated with cell survival and metastasis-related pathways. Our modeling approach comprehensively identifies key regulatory genes for drug resistance acquisition, enhancing our understanding of potential drug targets in breast cancer.

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

Posterior marginalization accelerates Bayesian inference for dynamical models of biological processes

Bayesian inference is an important method in the life and natural sciences for learning from data. It provides information about parameter and prediction uncertainties. Yet, generating representative samples from the posterior distribution is often computationally challenging. Here, we present an approach that lowers the computational complexity of sample generation for dynamical models with scaling, offset, and noise parameters. The proposed method is based on the marginalization of the posterior distribution. We provide analytical results for a broad class of problems with conjugate priors and show that the method is suitable for a large number of applications. Subsequently, we demonstrate the benefit of the approach for applications from the field of systems biology. We report an improvement up to 50 times in the effective sample size per unit of time. As the scheme is broadly applicable, it will facilitate Bayesian inference in different research fields.

Realistic simulation of time-course measurements in systems biology

In systems biology, the analysis of complex nonlinear systems faces many methodological challenges. For the evaluation and comparison of the performances of novel and competing computational methods, one major bottleneck is the availability of realistic test problems. We present an approach for performing realistic simulation studies for analyses of time course data as they are typically measured in systems biology. Since the design of experiments in practice depends on the process of interest, our approach considers the size and the dynamics of the mathematical model which is intended to be used for the simulation study. To this end, we used 19 published systems biology models with experimental data and evaluated the relationship between model features (e.g., the size and the dynamics) and features of the measurements such as the number and type of observed quantities, the number and the selection of measurement times, and the magnitude of measurement errors. Based on these typical relationships, our novel approach enables suggestions of realistic simulation study designs in the systems biology context and the realistic generation of simulated data for any dynamic model. The approach is demonstrated on three models in detail and its performance is validated on nine models by comparing ODE integration, parameter optimization, and parameter identifiability. The presented approach enables more realistic and less biased benchmark studies and thereby constitutes an important tool for the development of novel methods for dynamic modeling.

Straightforward model construction and analysis of multicomponent biomolecular systems in equilibrium

Mathematical modelling of molecular systems can be extremely helpful in elucidating complex phenomena in (bio)chemistry. However, equilibrium conditions in systems consisting of more than two components, such as for molecular glues bound to two proteins, can typically not be analytically determined without assumptions and (semi-)numerical models are not trivial to derive by the non-expert. Here we present a framework for equilibrium models, geared towards molecular glues and other contemporary multicomponent chemical biology challenges. The framework utilizes a general derivation method capable of generating custom mass-balance models for equilibrium conditions of complex molecular systems, based on the simple, reversible biomolecular reactions describing these systems. Several chemical biology concepts are revisited via the framework to demonstrate the simplicity, generality and validity of the approach. The ease of use of the framework and the ability to both analyze systems and gain additional insights in the underlying parameters driving equilibria formation strongly aids the analysis and understanding of biomolecular systems. New directions for research and analysis are brought forward based on the model formation and system and parameter analysis. This conceptual framework severely reduces the time and expertise requirements which currently impede the broad integration of such valuable equilibrium models into molecular glue development and chemical biology research.

Elucidating yeast glycolytic dynamics at steady state growth and glucose pulses through kinetic metabolic modeling

Microbial cell factories face changing environments during industrial fermentations. Kinetic metabolic models enable the simulation of the dynamic metabolic response to these perturbations, but their development is challenging due to model complexity and experimental data requirements. An example of this is the well-established microbial cell factory Saccharomyces cerevisiae, for which no consensus kinetic model of central metabolism has been developed and implemented in industry. Here, we aim to bring the academic and industrial communities closer to this consensus model. We developed a physiology informed kinetic model of yeast glycolysis connected to central carbon metabolism by including the effect of anabolic reactions precursors, mitochondria and the trehalose cycle. To parametrize such a large model, a parameter estimation pipeline was developed, consisting of a divide and conquer approach, supplemented with regularization and global optimization. Additionally, we show how this first mechanistic description of a growing yeast cell captures experimental dynamics at different growth rates and under a strong glucose perturbation, is robust to parametric uncertainty and explains the contribution of the different pathways in the network. Such a comprehensive model could not have been developed without using steady state and glucose perturbation data sets. The resulting metabolic reconstruction and parameter estimation pipeline can be applied in the future to study other industrially-relevant scenarios. We show this by generating a hybrid CFD-metabolic model to explore intracellular glycolytic dynamics for the first time. The model suggests that all intracellular metabolites oscillate within a physiological range, except carbon storage metabolism, which is sensitive to the extracellular environment.

Optimization of parameters in coherent spin dynamics of radical pairs in quantum biology

Identification of the external electromagnetic fields and internal hyperfine parameters which optimize the quantum singlet-triplet yield of simplified radical pairs modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. A method that combines sensitivity analysis with Tikhonov regularization is implemented. Numerical results demonstrate that the quantum singlet-triplet yield of the radical pair system can be significantly reduced if optimization is pursued simultaneously for both external magnetic fields and internal hyperfine parameters. The results may contribute towards understanding the structure-function relationship of a putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.

A Tiny Flexible Differential Tension Sensor

Modern applications of Internet of Things (IoT) devices require cheap and effective methods of measurement of physical quantities. Cheap IoT devices with sensor functionalities can detect a lack or excess of substances in everyday life or industry processes. One possible use of tension sensors in IoT applications is the automated replenishment process of fast moving consumer goods (FMCG) on shop shelves or home retail automation that allows for quick ordering of FMCG, where the IoT system is a part of smart packaging. For those reasons, a growing demand for cheap and tiny tension sensors has arisen. In this article, we propose a solution of a small flexible tension sensor fabricated in an amorphous InGaZnO (a-IGZO) thin-film process that can be integrated with other devices, e.g., near-field communications (NFC) or a barcode radio frequency identification (RFID) tag. The sensor was designed to magnify the slight internal changes in material properties caused by mechanical stress. These changes affect the dynamic electrical properties of specially designed inverters for a pair of ring oscillators, in which the frequencies become stress-dependent. In the article, we discuss and explain the approach to the optimum design of a ring oscillator that manifests the highest sensitivity to mechanical stress.

Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes ‘random’ latent factors affect the system in the ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises owing only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.

Mechanistic model of MAPK signaling reveals how allostery and rewiring contribute to drug resistance

BRAF is prototypical of oncogenes that can be targeted therapeutically and the treatment of BRAF^V600E melanomas with RAF and MEK inhibitors results in rapid tumor regression. However, drug-induced rewiring generates a drug adapted state thought to be involved in acquired resistance and disease recurrence. In this article, we study mechanisms of adaptive rewiring in BRAF^V600E melanoma cells using an energy-based implementation of ordinary differential equation (ODE) modeling in combination with proteomic, transcriptomic and imaging data. We develop a method for causal tracing of ODE models and identify two parallel MAPK reaction channels that are differentially sensitive to RAF and MEK inhibitors due to differences in protein oligomerization and drug binding. We describe how these channels, and timescale separation between immediate-early signaling and transcriptional feedback, create a state in which the RAS-regulated MAPK channel can be activated by growth factors under conditions in which the BRAF^V600E -driven channel is fully inhibited. Further development of the approaches in this article is expected to yield a unified model of adaptive drug resistance in melanoma.

Using Kinetic Modelling to Infer Adaptations in Saccharomyces cerevisiae Carbohydrate Storage Metabolism to Dynamic Substrate Conditions

Microbial metabolism is strongly dependent on the environmental conditions. While these can be well controlled under laboratory conditions, large-scale bioreactors are characterized by inhomogeneities and consequently dynamic conditions for the organisms. How Saccharomyces cerevisiae response to frequent perturbations in industrial bioreactors is still not understood mechanistically. To study the adjustments to prolonged dynamic conditions, we used published repeated substrate perturbation regime experimental data, extended it with proteomic measurements and used both for modelling approaches. Multiple types of data were combined; including quantitative metabolome, ¹³C enrichment and flux quantification data. Kinetic metabolic modelling was applied to study the relevant intracellular metabolic response dynamics. An existing model of yeast central carbon metabolism was extended, and different subsets of enzymatic kinetic constants were estimated. A novel parameter estimation pipeline based on combinatorial enzyme selection supplemented by regularization was developed to identify and predict the minimum enzyme and parameter adjustments from steady-state to dynamic substrate conditions. This approach predicted proteomic changes in hexose transport and phosphorylation reactions, which were additionally confirmed by proteome measurements. Nevertheless, the modelling also hints at a yet unknown kinetic or regulation phenomenon. Some intracellular fluxes could not be reproduced by mechanistic rate laws, including hexose transport and intracellular trehalase activity during substrate perturbation cycles.

Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks

Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical.

Estimation of Small-Scale Kinetic Parameters of Escherichia coli (E. coli) Model by Enhanced Segment Particle Swarm Optimization Algorithm ESe-PSO

The ability to create “structured models” of biological simulations is becoming more and more commonplace. Although computer simulations can be used to estimate the model, they are restricted by the lack of experimentally available parameter values, which must be approximated. In this study, an Enhanced Segment Particle Swarm Optimization (ESe-PSO) algorithm that can estimate the values of small-scale kinetic parameters is described and applied to E. coli’s main metabolic network as a model system. The glycolysis, phosphotransferase system, pentose phosphate, the TCA cycle, gluconeogenesis, glyoxylate pathways, and acetate formation pathways of Escherichia coli are represented by the Differential Algebraic Equations (DAE) system for the metabolic network. However, this algorithm uses segments to organize particle movements and the dynamic inertia weight (ω) to increase the algorithm’s exploration and exploitation potential. As an alternative to the state-of-the-art algorithm, this adjustment improves estimation accuracy. The numerical findings indicate a good agreement between the observed and predicted data. In this regard, the result of the ESe-PSO algorithm achieved superior accuracy compared with the Segment Particle Swarm Optimization (Se-PSO), Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Differential Evolution (DE) algorithms. As a result of this innovative approach, it was concluded that small-scale and even entire cell kinetic model parameters can be developed.

A Practical Guide for the Efficient Formulation and Calibration of Large, Energy- and Rule-Based Models of Cellular Signal Transduction

Aberrant signal transduction leads to complex diseases such as cancer. To rationally design treatment strategies with small molecule inhibitors, computational models have to be employed. Energy- and rule-based models allow the construction of mechanistic ordinary differential equation models based on structural insights. The detailed, energy-based description often generates large models, which are difficult to calibrate on experimental data. In this chapter, we provide a detailed, interactive protocol for the programmatic formulation and calibration of such large, energy- and rule-based models of cellular signal transduction based on an example model describing the action of RAF inhibitors on MAPK signaling. An interactive version of this chapter is available as Jupyter Notebook at github.com/FFroehlich/energy_modeling_chapter .

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Improving dynamic predictions with ensembles of observable models

MOTIVATION

Dynamic mechanistic modelling in systems biology has been hampered by the complexity and variability associated with the underlying interactions, and by uncertain and sparse experimental measurements. Ensemble modelling, a concept initially developed in statistical mechanics, has been introduced in biological applications with the aim of mitigating those issues. Ensemble modelling uses a collection of different models compatible with the observed data to describe the phenomena of interest. However, since systems biology models often suffer from a lack of identifiability and observability, ensembles of models are particularly unreliable when predicting non-observable states.

RESULTS

We present a strategy to assess and improve the reliability of a class of model ensembles. In particular, we consider kinetic models described using ordinary differential equations with a fixed structure. Our approach builds an ensemble with a selection of the parameter vectors found when performing parameter estimation with a global optimization metaheuristic. This technique enforces diversity during the sampling of parameter space and it can quantify the uncertainty in the predictions of state trajectories. We couple this strategy with structural identifiability and observability analysis, and when these tests detect possible prediction issues we obtain model reparameterizations that surmount them. The end result is an ensemble of models with the ability to predict the internal dynamics of a biological process. We demonstrate our approach with models of glucose regulation, cell division, circadian oscillations and the JAK-STAT signalling pathway.

AVAILABILITY AND IMPLEMENTATION

The code that implements the methodology and reproduces the results is available at https://doi.org/10.5281/zenodo.6782638.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

SBbadger: biochemical reaction networks with definable degree distributions

MOTIVATION

An essential step in developing computational tools for the inference, optimization and simulation of biochemical reaction networks is gauging tool performance against earlier efforts using an appropriate set of benchmarks. General strategies for the assembly of benchmark models include collection from the literature, creation via subnetwork extraction and de novo generation. However, with respect to biochemical reaction networks, these approaches and their associated tools are either poorly suited to generate models that reflect the wide range of properties found in natural biochemical networks or to do so in numbers that enable rigorous statistical analysis.

RESULTS

In this work, we present SBbadger, a python-based software tool for the generation of synthetic biochemical reaction or metabolic networks with user-defined degree distributions, multiple available kinetic formalisms and a host of other definable properties. SBbadger thus enables the creation of benchmark model sets that reflect properties of biological systems and generate the kinetics and model structures typically targeted by computational analysis and inference software. Here, we detail the computational and algorithmic workflow of SBbadger, demonstrate its performance under various settings, provide sample outputs and compare it to currently available biochemical reaction network generation software.

AVAILABILITY AND IMPLEMENTATION

SBbadger is implemented in Python and is freely available at https://github.com/sys-bio/SBbadger and via PyPI at https://pypi.org/project/SBbadger/. Documentation can be found at https://SBbadger.readthedocs.io.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (G_x) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of G_x estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of G_xs of the baseline model. G_xs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic G_xs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-G_x relationship during optimization revealed progressive convergence of the randomized population of G_xs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing G_xs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Evaluation of the Influence of Rootstock Type on the Yield Parameters of Vines Using a Mathematical Model in Nontraditional Wine-Growing Conditions

Great interest in viticulture in temperate climates results from the introduction of new interspecies hybrids of grapevines which are quite popular due to their high resistance to fungal diseases and lower temperature. However, the impact of rootstocks, common in vine cultivation, is little to not known, which makes setting up vineyards a challenge. This study aimed to evaluate the effect of the following six rootstock types: 101-14 Mgt, SORI, 161-49 C, 5 BB, SO4, 125 AA, and grapevines with their own roots on the yield quantity and berry quality (expressed by Brix extract) of Regent grapevines in temperate climates (southeastern Poland). A five-year experiment alongside a novel numerical model is applied to formulate precise and constructive findings about the rootstock impact in a temperate climate. Both the experimental and numerical part are supported by detailed statistical analysis. The five-year period of study indicates that the vines on rootstock 125 AA yielded the best, significantly. Shrubs grafted on rootstock 161-49 yielded the lowest, while the fruit extract content grafted on rootstock 101-14 was significantly lower among the evaluated ones. The parameters of own-rooted bushes and those grafted on SO4 rootstock did not differ significantly, except for the extract. The model leads to convergent conclusions with statistical analysis of raw experimental data. The 125 AA rootstock was the best for all nine tested case scenarios. On the other hand, 161-49 rootstock was the weakest, justified only in the most challenging conditions.

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.

Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation. We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.

Mathematical Modeling for the Industrial 2-Mercaptobenzothiazole Batch Production Process

As an important chemical intermediate, 2-mercaptobenzothiazole (MBT) is widely used in various processes, especially in the rubber industry. However, there is no first-principles model that describes the synthetic process of MBT. This paper focuses on the formulation of a reliable mathematical model represented by a series of differential and algebraic equations for the industrial batch MBT production process. It is difficult to estimate all of the unknown parameters in the model because of the lack of sufficient industrial/experimental data. Thus, a reduced estimable parameter set is derived by performing estimability analysis on the original estimation problem. A multiple-starting-point strategy is then applied to numerically solve the non-convex parameter estimation problem with the weighted least-squares approach. Subsequently, a cross-validation technique is employed to evaluate the generalizability of the proposed model. Finally, it is confirmed that the proposed model produces encouraging prediction performance with regard to independent test data.

Multi-Level Computational Modeling of Anti-Cancer Dendritic Cell Vaccination Utilized to Select Molecular Targets for Therapy Optimization

Dendritic cells (DCs) can be used for therapeutic vaccination against cancer. The success of this therapy depends on efficient tumor-antigen presentation to cytotoxic T lymphocytes (CTLs) and the induction of durable CTL responses by the DCs. Therefore, simulation of such a biological system by computational modeling is appealing because it can improve our understanding of the molecular mechanisms underlying CTL induction by DCs and help identify new strategies to improve therapeutic DC vaccination for cancer. Here, we developed a multi-level model accounting for the life cycle of DCs during anti-cancer immunotherapy. Specifically, the model is composed of three parts representing different stages of DC immunotherapy - the spreading and bio-distribution of intravenously injected DCs in human organs, the biochemical reactions regulating the DCs' maturation and activation, and DC-mediated activation of CTLs. We calibrated the model using quantitative experimental data that account for the activation of key molecular circuits within DCs, the bio-distribution of DCs in the body, and the interaction between DCs and T cells. We showed how such a data-driven model can be exploited in combination with sensitivity analysis and model simulations to identify targets for enhancing anti-cancer DC vaccination. Since other previous works show how modeling improves therapy schedules and DC dosage, we here focused on the molecular optimization of the therapy. In line with this, we simulated the effect in DC vaccination of the concerted modulation of combined intracellular regulatory processes and proposed several possibilities that can enhance DC-mediated immunogenicity. Taken together, we present a comprehensive time-resolved multi-level model for studying DC vaccination in melanoma. Although the model is not intended for personalized patient therapy, it could be used as a tool for identifying molecular targets for optimizing DC-based therapy for cancer, which ultimately should be tested in in vitro and in vivo experiments.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Mini-batch optimization enables training of ODE models on large-scale datasets

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

BACKGROUND

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws.

RESULTS

In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability.

CONCLUSIONS

We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Efficient gradient-based parameter estimation for dynamic models using qualitative data

MOTIVATION

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

RESULTS

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

AVAILABILITY AND IMPLEMENTATION

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States

Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. Given measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, these constants may be inferred by model fitting, but the estimation problems are hard to solve if models are large. Here we show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined from data if metabolic fluxes are known. The estimation method, called model balancing, can handle models with a wide range of rate laws and accounts for thermodynamic constraints between fluxes, kinetic constants, and metabolite concentrations. It can be used to estimate in-vivo kinetic constants, to complete and adjust available data, and to construct plausible metabolic states with predefined flux distributions. By omitting one term from the log posterior-a term for penalising low enzyme concentrations-we obtain a convex optimality problem with a unique local optimum. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in E. coli central metabolism. The example shows what information about kinetic constants can be obtained from omics data and reveals practical limits to estimating in-vivo kinetic constants. While noise-free omics data allow for a reasonable reconstruction of in-vivo kcat and KM values, prediction from noisy omics data are worse. Hence, adjusting kinetic constants and omics data to obtain consistent metabolic models is the main application of model balancing.

Fitting thermodynamic-based models: Incorporating parameter sensitivity improves the performance of an evolutionary algorithm

A detailed comprehension of transcriptional regulation is critical to understanding the genetic control of development and disease across many different organisms. To more fully investigate the complex molecular interactions controlling the precise expression of genes, many groups have constructed mathematical models to complement their experimental approaches. A critical step in such studies is choosing the most appropriate parameter estimation algorithm to enable detailed analysis of the parameters that contribute to the models. In this study, we develop a novel set of evolutionary algorithms that use a pseudo-random Sobol Set to construct the initial population and incorporate parameter sensitivities into the adaptation of mutation rates, using local, global, and hybrid strategies. Comparison of the performance of these new algorithms to a number of current state-of-the-art global parameter estimation algorithms on a range of continuous test functions, as well as synthetic biological data representing models of gene regulatory systems, reveals improved performance of the new algorithms in terms of runtime, error and reproducibility. In addition, by analyzing the ability of these algorithms to fit datasets of varying quality, we provide the experimentalist with a guide to how the algorithms perform across a range of noisy data. These results demonstrate the improved performance of the new set of parameter estimation algorithms and facilitate meaningful integration of model parameters and predictions in our understanding of the molecular mechanisms of gene regulation.

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Characterisation and quantification of nonlinearities in the engineering structures include selecting and fitting a good mathematical model to a set of experimental vibration data with significant nonlinear features. These tasks involve solving an optimisation problem where it is difficult to choose a priori the best optimisation technique. This paper presents a systematic comparison of ten optimisation methods used to select the best nonlinear model and estimate its parameters through nonlinear system identification. The model selection framework fits the structure’s equation of motions using time-domain dynamic response data and takes into account couplings due to the presence of the nonlinearities. Three benchmark problems are used to evaluate the performance of two families of optimisation methods: (i) deterministic local searches and (ii) global optimisation metaheuristics. Furthermore, hybrid local–global optimisation methods are examined. All benchmark problems include a free play nonlinearity commonly found in mechanical structures. Multiple performance criteria are considered based on computational efficiency and robustness, that is, finding the best nonlinear model. Results show that hybrid methods, that is, the multi-start strategy with local gradient-based Levenberg–Marquardt method and the particle swarm with Levenberg–Marquardt method, lead to a successful selection of nonlinear models and an accurate estimation of their parameters within acceptable computational times.

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.

Metabolic Modeling Combined With Machine Learning Integrates Longitudinal Data and Identifies the Origin of LXR-Induced Hepatic Steatosis

Temporal multi-omics data can provide information about the dynamics of disease development and therapeutic response. However, statistical analysis of high-dimensional time-series data is challenging. Here we develop a novel approach to model temporal metabolomic and transcriptomic data by combining machine learning with metabolic models. ADAPT (Analysis of Dynamic Adaptations in Parameter Trajectories) performs metabolic trajectory modeling by introducing time-dependent parameters in differential equation models of metabolic systems. ADAPT translates structural uncertainty in the model, such as missing information about regulation, into a parameter estimation problem that is solved by iterative learning. We have now extended ADAPT to include both metabolic and transcriptomic time-series data by introducing a regularization function in the learning algorithm. The ADAPT learning algorithm was (re)formulated as a multi-objective optimization problem in which the estimation of trajectories of metabolic parameters is constrained by the metabolite data and refined by gene expression data. ADAPT was applied to a model of hepatic lipid and plasma lipoprotein metabolism to predict metabolic adaptations that are induced upon pharmacological treatment of mice by a Liver X receptor (LXR) agonist. We investigated the excessive accumulation of triglycerides (TG) in the liver resulting in the development of hepatic steatosis. ADAPT predicted that hepatic TG accumulation after LXR activation originates for 80% from an increased influx of free fatty acids. The model also correctly estimated that TG was stored in the cytosol rather than transferred to nascent very-low density lipoproteins. Through model-based integration of temporal metabolic and gene expression data we discovered that increased free fatty acid influx instead of de novo lipogenesis is the main driver of LXR-induced hepatic steatosis. This study illustrates how ADAPT provides estimates for biomedically important parameters that cannot be measured directly, explaining (side-)effects of pharmacological treatment with LXR agonists.

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

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.

Systems biology informed deep learning for inferring parameters and hidden dynamics

Mathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems.

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

Benchmark problems for dynamic modeling of intracellular processes

Motivation

Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A multitude of computational approaches, e.g. for parameter estimation or uncertainty analysis have been developed within recent years. However, many of these approaches lack proper testing in application settings because a comprehensive set of benchmark problems is yet missing.

Results

We present a collection of 20 benchmark problems in order to evaluate new and existing methodologies, where an ODE model with corresponding experimental data is referred to as problem. In addition to the equations of the dynamical system, the benchmark collection provides observation functions as well as assumptions about measurement noise distributions and parameters. The presented benchmark models comprise problems of different size, complexity and numerical demands. Important characteristics of the models and methodological requirements are summarized, estimated parameters are provided, and some example studies were performed for illustrating the capabilities of the presented benchmark collection.

Availability and implementation

The models are provided in several standardized formats, including an easy-to-use human readable form and machine-readable SBML files. The data is provided as Excel sheets. All files are available at https://github.com/Benchmarking-Initiative/Benchmark-Models, including step-by-step explanations and MATLAB code to process and simulate the models.

Supplementary information

Supplementary data are available at Bioinformatics online.

Global optimization of the Michaelis-Menten parameters using physiologically-based pharmacokinetic (PBPK) modeling and chloroform vapor uptake data in F344 rats

Objective: To quantify metabolism, a physiologically based pharmacokinetic (PBPK) model for a volatile compound can be calibrated with the closed chamber (i.e. vapor uptake) inhalation data. Here, we introduce global optimization as a novel component of the predictive process and use it to illustrate a procedure for metabolic parameter estimation.Materials and methods: Male F344 rats were exposed in vapor uptake chambers to initial concentrations of 100, 500, 1000, and 3000 ppm chloroform. Chamber time-course data from these experiments, in combination with optimization using a chemical-specific PBPK model, were used to estimate Michaelis-Menten metabolic constants. Matlab^® simulation software was used to integrate the mass balance equations and to perform the global optimizations using MEIGO (MEtaheuristics for systems biology and bIoinformatics Global Optimization - Version 64 bit, R2016A), a toolbox written for Matlab®. The cost function used the chamber time-course data and least squares to minimize the difference between data and simulation values.Results and discussion: The final values estimated for V_max (maximum metabolic rate) and K_m (affinity constant) were 1.2 mg/h and a range between 0.0005 and 0.6 mg/L, respectively. Also, cost function plots were used to analyze the dose-dependent capacity to estimate V_max and K_m within the experimental range used. Sensitivity analysis was used to assess identifiability for both parameters and show these kinetic data may not be sufficient to identify K_m.Conclusion: In summary, this work should help toxicologists interested in optimization techniques understand the overall process employed when calibrating metabolic parameters in a PBPK model with inhalation data.

Model-based analysis of response and resistance factors of cetuximab treatment in gastric cancer cell lines

Targeted cancer therapies are powerful alternatives to chemotherapies or can be used complementary to these. Yet, the response to targeted treatments depends on a variety of factors, including mutations and expression levels, and therefore their outcome is difficult to predict. Here, we develop a mechanistic model of gastric cancer to study response and resistance factors for cetuximab treatment. The model captures the EGFR, ERK and AKT signaling pathways in two gastric cancer cell lines with different mutation patterns. We train the model using a comprehensive selection of time and dose response measurements, and provide an assessment of parameter and prediction uncertainties. We demonstrate that the proposed model facilitates the identification of causal differences between the cell lines. Furthermore, our study shows that the model provides predictions for the responses to different perturbations, such as knockdown and knockout experiments. Among other results, the model predicted the effect of MET mutations on cetuximab sensitivity. These predictive capabilities render the model a basis for the assessment of gastric cancer signaling and possibly for the development and discovery of predictive biomarkers.

Unraveling the causal differences between drug responders and non-responders is an important challenge. The information can help to understand molecular mechanisms and to guide the selection and design of targeted therapies. Here, we approach this problem for cetuximab treatment for gastric cancer using mechanistic mathematical modeling. The proposed model describes responder and non-responder gastric cancer cell lines and can predict the response in several validation experiments. Our analysis provides a differentiated view on mutations and explains, for instance, the relevance of MET mutations and the insignificance of PIK3CA mutation in the considered cell lines. The model might potentially provide the basis for understanding the recent failure of several clinical studies.

Guidelines for benchmarking of optimization-based approaches for fitting mathematical models

Insufficient performance of optimization-based approaches for the fitting of mathematical models is still a major bottleneck in systems biology. In this article, the reasons and methodological challenges are summarized as well as their impact in benchmark studies. Important aspects for achieving an increased level of evidence for benchmark results are discussed. Based on general guidelines for benchmarking in computational biology, a collection of tailored guidelines is presented for performing informative and unbiased benchmarking of optimization-based fitting approaches. Comprehensive benchmark studies based on these recommendations are urgently required for the establishment of a robust and reliable methodology for the systems biology community.