Predicting ligand-dependent tumors from multi-dimensional signaling features

Long-Term Single-Molecule Tracking in Living Cells using Weak-Affinity Protein Labeling

Single-particle tracking (SPT) has become a powerful tool to monitor the dynamics of membrane proteins in living cells. However, permanent labeling strategies for SPT suffer from photobleaching as a major limitation, restricting observation times, and obstructing the study of long-term cellular processes within single living cells. Here, we use exchangeable HaloTag Ligands (xHTLs) as an easy-to-apply labeling approach for live-cell SPT and demonstrate extended observation times of individual living cells of up to 30 minutes. Using the xHTL/HaloTag7 labeling system, we measure the ligand-induced activation kinetics of the epidermal growth factor receptor (EGFR) in single living cells. We generate spatial maps of receptor diffusion in cells, report non-uniform distributions of receptor mobility, and the formation of spatially confined 'hot spots' of EGFR activation. Furthermore, we measured the mobility of an ER-luminal protein in living cells and found diffusion coefficients that correlated with the ER nano-structure. This approach represents a general strategy to monitor protein mobility in a functional context and for extended observation times in single living cells.

DynProfiler: a Python package for comprehensive analysis and interpretation of signaling dynamics leveraged by deep learning techniques

Summary

Signaling dynamics encode important features and regulatory mechanisms of biological systems, and recent studies have reported the use of simulated signaling dynamics with mechanistic modeling as biomarkers for human diseases. Given the success of deep learning techniques, it is expected that they can extract informative patterns from simulation results more effectively than traditional approaches involving manual feature selection, which can be used for subsequent analyses, such as patient stratification and survival prediction. Here, we propose DynProfiler, which utilizes the entire signaling dynamics, including intermediate variables, as input and leverages deep learning techniques to extract informative features without requiring any labels. Furthermore, DynProfiler incorporates a modern explainable AI solution to provide quantitative time-dependent importance scores for each dynamics. Using simulated dynamics of patients with breast cancer as an example, we demonstrate DynProfiler's ability to extract high-quality features that can predict mortality risk and identify important dynamics, highlighting upregulated phosphorylated GSK3β as a biomarker for poor prognosis. Overall, this tool can be useful for clinical application, as well as for elucidating biological system dynamics.

Availability and implementation

The DynProfiler Python library is available in GitHub at https://github.com/okadalabipr/DynProfiler.

Mechanistic modeling of cell viability assays with in silico lineage tracing

Data from cell viability assays, which measure cumulative division and death events in a population and reflect substantial cellular heterogeneity, are widely available. However, interpreting such data with mechanistic computational models is hindered because direct model/data comparison is often muddled. We developed an algorithm that tracks simulated division and death events in mechanistically detailed single-cell lineages to enable such a model/data comparison and suggest causes of cell-cell drug response variability. Using our previously developed model of mammalian single-cell proliferation and death signaling, we simulated drug dose response experiments for four targeted anti-cancer drugs (alpelisib, neratinib, trametinib and palbociclib) and compared them to experimental data. Simulations are consistent with data for strong growth inhibition by trametinib (MEK inhibitor) and overall lack of efficacy for alpelisib (PI-3K inhibitor), but are inconsistent with data for palbociclib (CDK4/6 inhibitor) and neratinib (EGFR inhibitor). Model/data inconsistencies suggest (i) the importance of CDK4/6 for driving the cell cycle may be overestimated, and (ii) that the cellular balance between basal (tonic) and ligand-induced signaling is a critical determinant of receptor inhibitor response. Simulations show subpopulations of rapidly and slowly dividing cells in both control and drug-treated conditions. Variations in mother cells prior to drug treatment all impinging on ERK pathway activity are associated with the rapidly dividing phenotype and trametinib resistance. This work lays a foundation for the application of mechanistic modeling to large-scale cell viability assay datasets and better understanding determinants of cellular heterogeneity in drug response.

Efficient parameter estimation for ODE models of cellular processes using semi-quantitative data

MOTIVATION

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. The parameters of these models are commonly estimated from experimental data. Yet, experimental data generated from different techniques do not provide direct information about the state of the system but a nonlinear (monotonic) transformation of it. For such semi-quantitative data, when this transformation is unknown, it is not apparent how the model simulations and the experimental data can be compared.

RESULTS

We propose a versatile spline-based approach for the integration of a broad spectrum of semi-quantitative data into parameter estimation. We derive analytical formulas for the gradients of the hierarchical objective function and show that this substantially increases the estimation efficiency. Subsequently, we demonstrate that the method allows for the reliable discovery of unknown measurement transformations. Furthermore, we show that this approach can significantly improve the parameter inference based on semi-quantitative data in comparison to available methods.

AVAILABILITY AND IMPLEMENTATION

Modelers can easily apply our method by using our implementation in the open-source Python Parameter EStimation TOolbox (pyPESTO) available at https://github.com/ICB-DCM/pyPESTO.

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.

Uncovering specific mechanisms across cell types in dynamical models

Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements.

Biased activation of the receptor tyrosine kinase HER2

HER2 belongs to the ErbB sub-family of receptor tyrosine kinases and regulates cellular proliferation and growth. Different from other ErbB receptors, HER2 has no known ligand. Activation occurs through heterodimerization with other ErbB receptors and their cognate ligands. This suggests several possible activation paths of HER2 with ligand-specific, differential response, which has so far remained unexplored. Using single-molecule tracking and the diffusion profile of HER2 as a proxy for activity, we measured the activation strength and temporal profile in live cells. We found that HER2 is strongly activated by EGFR-targeting ligands EGF and TGFα, yet with a distinguishable temporal fingerprint. The HER4-targeting ligands EREG and NRGβ1 showed weaker activation of HER2, a preference for EREG, and a delayed response to NRGβ1. Our results indicate a selective ligand response of HER2 that may serve as a regulatory element. Our experimental approach is easily transferable to other membrane receptors targeted by multiple ligands.

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.

Disentangling ERBB Signaling in Breast Cancer Subtypes-A Model-Based Analysis

Targeted therapies have shown striking success in the treatment of cancer over the last years. However, their specific effects on an individual tumor appear to be varying and difficult to predict. Using an integrative modeling approach that combines mechanistic and regression modeling, we gained insights into the response mechanisms of breast cancer cells due to different ligand-drug combinations. The multi-pathway model, capturing ERBB receptor signaling as well as downstream MAPK and PI3K pathways was calibrated on time-resolved data of the luminal breast cancer cell lines MCF7 and T47D across an array of four ligands and five drugs. The same model was then successfully applied to triple negative and HER2-positive breast cancer cell lines, requiring adjustments mostly for the respective receptor compositions within these cell lines. The additional relevance of cell-line-specific mutations in the MAPK and PI3K pathway components was identified via L1 regularization, where the impact of these mutations on pathway activation was uncovered. Finally, we predicted and experimentally validated the proliferation response of cells to drug co-treatments. We developed a unified mathematical model that can describe the ERBB receptor and downstream signaling in response to therapeutic drugs targeting this clinically relevant signaling network in cell line that represent three major subtypes of breast cancer. Our data and model suggest that alterations in this network could render anti-HER therapies relevant beyond the HER2-positive subtype.

A text-based computational framework for patient -specific modeling for classification of cancers

Patient heterogeneity precludes cancer treatment and drug development; hence, development of methods for finding prognostic markers for individual treatment is urgently required. Here, we present Pasmopy (Patient-Specific Modeling in Python), a computational framework for stratification of patients using in silico signaling dynamics. Pasmopy converts texts and sentences on biochemical systems into an executable mathematical model. Using this framework, we built a model of the ErbB receptor signaling network, trained in cultured cell lines, and performed in silico simulation of 377 patients with breast cancer using The Cancer Genome Atlas (TCGA) transcriptome datasets. The temporal dynamics of Akt, extracellular signal-regulated kinase (ERK), and c-Myc in each patient were able to accurately predict the difference in prognosis and sensitivity to kinase inhibitors in triple-negative breast cancer (TNBC). Our model applies to any type of signaling network and facilitates the network-based use of prognostic markers and prediction of drug response.

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A text file describing biochemical systems is converted into an executable model

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Patient-specific models incorporate individual gene expression profiles

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In silico signaling dynamics can be utilized as prognostic biomarkers

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Personalized kinetic models are capable of predicting potential drug targets

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.

Functional signaling test identifies HER2 negative breast cancer patients who may benefit from c-Met and pan-HER combination therapy

Background

Research is revealing the complex coordination between cell signaling systems as they adapt to genetic and epigenetic changes. Tools to uncover these highly complex functional linkages will play an important role in advancing more efficacious disease treatments. Current tumor cell signal transduction research is identifying coordination between receptor types, receptor families, and transduction pathways to maintain tumor cell viability despite challenging tumor microenvironment conditions.

Methods

In this report, coactivated abnormal levels of signaling activity for c-Met and HER family receptors in live tumor cells were measured by a new clinical test to identify a subpopulation of breast cancer patients that could be responsive to combined targeted therapies. The CELsignia Multi-Pathway Signaling Function (CELsignia) Test uses an impedance biosensor to quantify an individual patient’s ex vivo live tumor cell signaling response in real-time to specific HER family and c-Met co-stimulation and targeted therapies.

Results

The test identified breast tumors with hyperactive HER1, HER2, HER3/4, and c-Met coordinated signaling that express otherwise normal amounts of these receptors. The supporting data of the pre-clinical verification of this test included analyses of 79 breast cancer patients’ cell response to HER and c-Met agonists. The signaling results were confirmed using clinically approved matching targeted drugs, and combinations of targeted drugs in addition to correlative mouse xenograft tumor response to HER and c-Met targeted therapies.

Conclusions

The results of this study demonstrated the potential benefit of a functional test for identifying a subpopulation of breast cancer patients with coordinated abnormal HER and c-Met signaling for a clinical trial testing combination targeted therapy.

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.

MECHANISTIC AND DATA-DRIVEN MODELS OF CELL SIGNALING: TOOLS FOR FUNDAMENTAL DISCOVERY AND RATIONAL DESIGN OF THERAPY

A full understanding of cell signaling processes requires knowledge of protein structure/function relationships, protein-protein interactions, and the abilities of pathways to control phenotypes. Computational models offer a valuable framework for integrating that knowledge to predict the effects of system perturbations and interventions in health and disease. Whereas mechanistic models are well suited for understanding the biophysical basis for signal transduction and principles of therapeutic design, data-driven models are particularly suited to distill complex signaling relationships among samples and between multivariate signaling changes and phenotypes. Both approaches have limitations and provide incomplete representations of signaling biology, but their careful implementation and integration can provide new understanding for how manipulating system variables impacts cellular decisions.

Deciphering the signaling network of breast cancer improves drug sensitivity prediction

One goal of precision medicine is to tailor effective treatments to patients' specific molecular markers of disease. Here, we used mass cytometry to characterize the single-cell signaling landscapes of 62 breast cancer cell lines and five lines from healthy tissue. We quantified 34 markers in each cell line upon stimulation by the growth factor EGF in the presence or absence of five kinase inhibitors. These data-on more than 80 million single cells from 4,000 conditions-were used to fit mechanistic signaling network models that provide insight into how cancer cells process information. Our dynamic single-cell-based models accurately predicted drug sensitivity and identified genomic features associated with drug sensitivity, including a missense mutation in DDIT3 predictive of PI3K-inhibition sensitivity. We observed similar trends in genotype-drug sensitivity associations in patient-derived xenograft mouse models. This work provides proof of principle that patient-specific single-cell measurements and modeling could inform effective precision medicine strategies.

Building patient-specific models for receptor tyrosine kinase signaling networks

Cancer progresses due to changes in the dynamic interactions of multidimensional factors associated with gene mutations. Cancer research has actively adopted computational methods, including data-driven and mathematical model-driven approaches, to identify causative factors and regulatory rules that can explain the complexity and diversity of cancers. A data-driven, statistics-based approach revealed correlations between gene alterations and clinical outcomes in many types of cancers. A model-driven mathematical approach has elucidated the dynamic features of cancer networks and identified the mechanisms of drug efficacy and resistance. More recently, machine learning methods have emerged that can be used for mining omics data and classifying patient. However, as the strengths and weaknesses of each method becoming apparent, new analytical tools are emerging to combine and improve the methodologies and maximize their predictive power for classifying cancer subtypes and prognosis. Here, we introduce recent advances in cancer systems biology aimed at personalized medicine, with focus on the receptor tyrosine kinase signaling network.

A Computational Framework for Prediction and Analysis of Cancer Signaling Dynamics from RNA Sequencing Data-Application to the ErbB Receptor Signaling Pathway

Simple Summary

Temporal signaling dynamics are important for controlling the fate decisions of mammalian cells. In this study, we developed BioMASS, a computational platform for prediction and analysis of signaling dynamics using RNA-sequencing gene expression data. We first constructed a detailed mechanistic model of early transcriptional regulation mediated by ErbB receptor signaling pathway. After training the model parameters against phosphoprotein time-course datasets obtained from breast cancer cell lines, the model successfully predicted signaling activities of another untrained cell line. The result indicates that the parameters of molecular interactions in these different cell types are not particularly unique to the cell type, and the expression levels of the components of the signaling network are sufficient to explain the complex dynamics of the networks. Our method can be further expanded to predict signaling activity from clinical gene expression data for in silico drug screening for personalized medicine.

Abstract

A current challenge in systems biology is to predict dynamic properties of cell behaviors from public information such as gene expression data. The temporal dynamics of signaling molecules is critical for mammalian cell commitment. We hypothesized that gene expression levels are tightly linked with and quantitatively control the dynamics of signaling networks regardless of the cell type. Based on this idea, we developed a computational method to predict the signaling dynamics from RNA sequencing (RNA-seq) gene expression data. We first constructed an ordinary differential equation model of ErbB receptor → c-Fos induction using a newly developed modeling platform BioMASS. The model was trained with kinetic parameters against multiple breast cancer cell lines using autologous RNA-seq data obtained from the Cancer Cell Line Encyclopedia (CCLE) as the initial values of the model components. After parameter optimization, the model proceeded to prediction in another untrained breast cancer cell line. As a result, the model learned the parameters from other cells and was able to accurately predict the dynamics of the untrained cells using only the gene expression data. Our study suggests that gene expression levels of components within the ErbB network, rather than rate constants, can explain the cell-specific signaling dynamics, therefore playing an important role in regulating cell fate.

Imaging the fibroblast growth factor receptor network on the plasma membrane with DNA-assisted single-molecule super-resolution microscopy

Fibroblast growth factor receptors (FGFRs) are a subfamily of receptor tyrosine kinases and central players in health and disease. Following ligand binding and the formation of homo- and heteromeric complexes, FGFRs initiate a cellular response. Challenges in studying FGFR activation are inner-subfamily interactions and a complex heterogeneity of these in the cell membrane, which demand for observation techniques that can resolve individual protein complexes and that are compatible with endogenous protein levels. Here, we established an imaging and analysis pipeline for multiplexed single-molecule localization microscopy (SMLM) of the FGFR network at the plasma membrane. Using DNA-labeled primary antibodies, we visualize all four FGFRs in the same cell with near-molecular spatial resolution. From the super-resolution imaging data, we extract information on FGFR density, spatial distribution, and inner-subfamily colocalization. Our approach is straightforward and easily adaptable to other multiplexed SMLM data of membrane proteins.

Single-Molecule Super-Resolution Microscopy Reveals Heteromeric Complexes of MET and EGFR upon Ligand Activation

Receptor tyrosine kinases (RTKs) orchestrate cell motility and differentiation. Deregulated RTKs may promote cancer and are prime targets for specific inhibitors. Increasing evidence indicates that resistance to inhibitor treatment involves receptor cross-interactions circumventing inhibition of one RTK by activating alternative signaling pathways. Here, we used single-molecule super-resolution microscopy to simultaneously visualize single MET and epidermal growth factor receptor (EGFR) clusters in two cancer cell lines, HeLa and BT-20, in fixed and living cells. We found heteromeric receptor clusters of EGFR and MET in both cell types, promoted by ligand activation. Single-protein tracking experiments in living cells revealed that both MET and EGFR respond to their cognate as well as non-cognate ligands by slower diffusion. In summary, for the first time, we present static as well as dynamic evidence of the presence of heteromeric clusters of MET and EGFR on the cell membrane that correlates with the relative surface expression levels of the two receptors.

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.

Learning stable and predictive structures in kinetic systems

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well-established approaches focusing solely on predictive performance, especially for out-of-sample generalization.

Mechanistically detailed systems biology modeling of the HGF/Met pathway in hepatocellular carcinoma

Hepatocyte growth factor (HGF) signaling through its receptor Met has been implicated in hepatocellular carcinoma tumorigenesis and progression. Met interaction with integrins is shown to modulate the downstream signaling to Akt and ERK (extracellular-regulated kinase). In this study, we developed a mechanistically detailed systems biology model of HGF/Met signaling pathway that incorporated specific interactions with integrins to investigate the efficacy of integrin-binding peptide, AXT050, as monotherapy and in combination with other therapeutics targeting this pathway. Here we report that the modeled dynamics of the response to AXT050 revealed that receptor trafficking is sufficient to explain the effect of Met-integrin interactions on HGF signaling. Furthermore, the model predicted patient-specific synergy and antagonism of efficacy and potency for combination of AXT050 with sorafenib, cabozantinib, and rilotumumab. Overall, the model provides a valuable framework for studying the efficacy of drugs targeting receptor tyrosine kinase interaction with integrins, and identification of synergistic drug combinations for the patients.

Efficient parameterization of large-scale dynamic models based on relative measurements

MOTIVATION

Mechanistic models of biochemical reaction networks facilitate the quantitative understanding of biological processes and the integration of heterogeneous datasets. However, some biological processes require the consideration of comprehensive reaction networks and therefore large-scale models. Parameter estimation for such models poses great challenges, in particular when the data are on a relative scale.

RESULTS

Here, we propose a novel hierarchical approach combining (i) the efficient analytic evaluation of optimal scaling, offset and error model parameters with (ii) the scalable evaluation of objective function gradients using adjoint sensitivity analysis. We evaluate the properties of the methods by parameterizing a pan-cancer ordinary differential equation model (>1000 state variables, >4000 parameters) using relative protein, phosphoprotein and viability measurements. The hierarchical formulation improves optimizer performance considerably. Furthermore, we show that this approach allows estimating error model parameters with negligible computational overhead when no experimental estimates are available, providing an unbiased way to weight heterogeneous data. Overall, our hierarchical formulation is applicable to a wide range of models, and allows for the efficient parameterization of large-scale models based on heterogeneous relative measurements.

AVAILABILITY AND IMPLEMENTATION

Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3254429 and http://doi.org/10.5281/zenodo.3254441.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Extensions of ℓ1 regularization increase detection specificity for cell-type specific parameters in dynamic models

BACKGROUND

Ordinary differential equation systems are frequently utilized to model biological systems and to infer knowledge about underlying properties. For instance, the development of drugs requires the knowledge to which extent malign cells differ from healthy ones to provide a specific treatment with least side effects. As these cell-type specific properties may stem from any part of biochemical cell processes, systematic quantitative approaches are necessary to identify the relevant potential drug targets. An ℓ₁ regularization for the maximum likelihood parameter estimation proved to be successful, but falsely predicted cell-type dependent behaviour had to be corrected manually by using a Profile Likelihood approach.

RESULTS

The choice of extended ℓ₁ penalty functions significantly decreased the number of falsely detected cell-type specific parameters. Thus, the total accuracy of the prediction could be increased. This was tested on a realistic dynamical benchmark model used for the DREAM6 challenge. Among Elastic Net, Adaptive Lasso and a non-convex ℓ_q penalty, the latter one showed the best predictions whilst also requiring least computation time. All extended methods include a hyper-parameter in the regularization function. For an Erythropoietin (EPO) induced signalling pathway, the extended methods ℓ_q and Adaptive Lasso revealed an unpublished alternative parsimonious model when varying the respective hyper-parameters.

CONCLUSIONS

Using ℓ_q or Adaptive Lasso with an a-priori choice for the hyper-parameter can lead to a more specific and accurate result than ℓ₁. Scanning different hyper-parameters can yield additional pieces of information about the system.

Community-driven roadmap for integrated disease maps

The Disease Maps Project builds on a network of scientific and clinical groups that exchange best practices, share information and develop systems biomedicine tools. The project aims for an integrated, highly curated and user-friendly platform for disease-related knowledge. The primary focus of disease maps is on interconnected signaling, metabolic and gene regulatory network pathways represented in standard formats. The involvement of domain experts ensures that the key disease hallmarks are covered and relevant, up-to-date knowledge is adequately represented. Expert-curated and computer readable, disease maps may serve as a compendium of knowledge, allow for data-supported hypothesis generation or serve as a scaffold for the generation of predictive mathematical models. This article summarizes the 2nd Disease Maps Community meeting, highlighting its important topics and outcomes. We outline milestones on the roadmap for the future development of disease maps, including creating and maintaining standardized disease maps; sharing parts of maps that encode common human disease mechanisms; providing technical solutions for complexity management of maps; and Web tools for in-depth exploration of such maps. A dedicated discussion was focused on mathematical modeling approaches, as one of the main goals of disease map development is the generation of mathematically interpretable representations to predict disease comorbidity or drug response and to suggest drug repositioning, altogether supporting clinical decisions.

Dynamic Targeting in Cancer Treatment

With the advent of personalized medicine, design and development of anti-cancer drugs that are specifically targeted to individual or sets of genes or proteins has been an active research area in both academia and industry. The underlying motivation for this approach is to interfere with several pathological crosstalk pathways in order to inhibit or at the very least control the proliferation of cancer cells. However, after initially conferring beneficial effects, if sub-lethal, these artificial perturbations in cell function pathways can inadvertently activate drug-induced up- and down-regulation of feedback loops, resulting in dynamic changes over time in the molecular network structure and potentially causing drug resistance as seen in clinics. Hence, the targets or their combined signatures should also change in accordance with the evolution of the network (reflected by changes to the structure and/or functional output of the network) over the course of treatment. This suggests the need for a "dynamic targeting" strategy aimed at optimizing tumor control by interfering with different molecular targets, at varying stages. Understanding the dynamic changes of this complex network under various perturbed conditions due to drug treatment is extremely challenging under experimental conditions let alone in clinical settings. However, mathematical modeling can facilitate studying these effects at the network level and beyond, and also accelerate comparison of the impact of different dosage regimens and therapeutic modalities prior to sizeable investment in risky and expensive clinical trials. A dynamic targeting strategy based on the use of mathematical modeling can be a new, exciting research avenue in the discovery and development of therapeutic drugs.

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

A scientist engineer's contribution to therapeutic discovery and development

An engineering perspective views cells as complex circuits that process inputs – drugs, environmental cues – to create complex outcomes – disease, growth, death – and this perspective has immense potential for drug development. Logical rules can describe the features of cells and reductionist approaches have exploited these rules for drug development. In contrast, the reductionist approach serially characterizes cellular components and develops a deep understanding of each component’s specific role. This approach underutilizes the full system of biomolecules relevant to disease pathology and drug effects. An engineering perspective provides the tools to understand and leverage the full extent of biological systems; applying both reverse and forward engineering, a strength of the engineering approach has demonstrated progress in advancing understanding of disease and drug mechanisms. Drug development lacks sufficient engineering specifications, or empirical models, of drug pharmacodynamic effects and future efforts to derive empirical models of drug effects will streamline this development. At this stage of progress, the scientist engineer is uniquely poised to solve problems in therapeutics related to modulating multiple diseases with a single or multiple therapeutic agents and identifying pharmacodynamics biomarkers with knowledge of drug pathways. This article underscores the value of these principles in an age where drug development costs are soaring and finding efficacious therapies is challenging.

Modeling chemotherapy-induced stress to identify rational combination therapies in the DNA damage response pathway

Cells respond to DNA damage by activating complex signaling networks that decide cell fate, promoting not only DNA damage repair and survival but also cell death. We have developed a multiscale computational model that quantitatively links chemotherapy-induced DNA damage response signaling to cell fate. The computational model was trained and calibrated on extensive data from U2OS osteosarcoma cells, including the cell cycle distribution of the initial cell population, signaling data measured by Western blotting, and cell fate data in response to chemotherapy treatment measured by time-lapse microscopy. The resulting mechanistic model predicted the cellular responses to chemotherapy alone and in combination with targeted inhibitors of the DNA damage response pathway, which we confirmed experimentally. Computational models such as the one presented here can be used to understand the molecular basis that defines the complex interplay between cell survival and cell death and to rationally identify chemotherapy-potentiating drug combinations.

Optimization and profile calculation of ODE models using second order adjoint sensitivity analysis

Motivation

Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with the number of state variables and quadratically with the number of parameters. This limits their application to low-dimensional problems.

Results

We introduce second order adjoint sensitivity analysis for the computation of Hessians and a hybrid optimization-integration-based approach for profile likelihood computation. Second order adjoint sensitivity analysis scales linearly with the number of parameters and state variables. The Hessians are effectively exploited by the proposed profile likelihood computation approach. We evaluate our approaches on published biological models with real measurement data. Our study reveals an improved computational efficiency and robustness of optimization compared to established approaches, when using Hessians computed with adjoint sensitivity analysis. The hybrid computation method was more than 2-fold faster than the best competitor. Thus, the proposed methods and implemented algorithms allow for the improvement of parameter estimation for medium and large scale ODE models.

Availability and implementation

The algorithms for second order adjoint sensitivity analysis are implemented in the Advanced MATLAB Interface to CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI/). The algorithm for hybrid profile likelihood computation is implemented in the parameter estimation toolbox (PESTO, https://github.com/ICB-DCM/PESTO/). Both toolboxes are freely available under the BSD license.

Supplementary information

Supplementary data are available at Bioinformatics online.