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Quantitative Systems Pharmacology models as a key to translational medicine
Journal Pre-proof Quantitative Systems Pharmacology Models as a Key to Translational Medicine Birgit Schoeberl PII:
S2452-3100(19)30035-6
DOI:
https://doi.org/10.1016/j.coisb.2019.10.019
Reference:
COISB 270
To appear in:
Current Opinion in Systems Biology
Received Date: 1 July 2019 Revised Date:
31 October 2019
Accepted Date: 31 October 2019
Please cite this article as: Schoeberl, B, Quantitative Systems Pharmacology Models as a Key to Translational Medicine, Current Opinion in Systems Biology, https://doi.org/10.1016/j.coisb.2019.10.019. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Quantitative Systems Pharmacology Models as a Key to Translational Medicine Birgit Schoeberl Novartis Institutes of Biomedical Research, 220 Massachusetts Ave. Cambridge MA 02139 [email protected]
Highlights: •
Quantitative Systems Pharmacology models are multi-scale with respect to time, space and species and a foundation of translational medicine.
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The complexity of multi-scale models is defined by the scientific question.
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Complex multi-scale models are regarded with skepticism based on the potential for human error and many unknown parameters.
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Opportunity for the community to address the challenges of multi-scale models: o
Develop tools to enable more efficient model building
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Improve model and data sharing,
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Develop best practices for model validation
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Advance computational frameworks to enable large scale parameter optimization
Abstract Recent advances in experimentation and computation have allowed us to build multi-scale models of unprecedented scale. Quantitative Systems Pharmacology (QSP) models are multi-scale models that link protein- or drug- interaction kinetics to cellular response in the context of animal or human (disease) physiology. One of the areas where QSP models hold the most promise, is in translating preclinical science into the clinic. In the following, I discuss recent examples of multi-scale models such as bacterial whole cell models, multi-scale tumor growth inhibition models to assess possible drug combinations and human disease models. Challenges of multi-scale models and emerging solutions will be discussed.
Introduction Knowing the biological building blocks is not sufficient for understanding health and disease. Biological function does not exclusively originate at the level of the gene but is determined by positive and negative feedback regulations between gene, RNA, protein and external cues. This inherent complexity necessitates the development of mathematical models that bridge different scales (time, molecules to organisms and across species). These models incorporate prior knowledge and are based on very diverse sets of experimental data. Advances in both high-throughput experimentation and computational power have opened up the possibility of creating and analyzing more complex dynamic models of biological systems (Hasenauer et al. 2015). Statistical and machine learning methods represent accessible options to analyze large scale data-sets. Statistical approaches are at the forefront of predicting drug sensitivity by linking genomic and proteomic information to drug sensitivity (Ali et al. 2018), (Li, Shi, and Liang 2019), (Niz et al. 2016). However, machine learning models are limited in their ability to extrapolate predictions into untrained regimes, to make longitudinal predictions or to explain causality. More generally, they still face challenges in their clinical applicability (Fröhlich et al. 2018). The field of Systems Biology developed in the early 2000s as a framework for assembling models of biological systems from systematic measurements (Chuang, Hofree, and Ideker 2010). Systems Biology models often focus on the understanding of how cells translate external signals into (phenotypic) responses (Alkan et al. 2018),(Hass et al. 2017),(Ryu et al. 2015). However, Systems Biology with its focus on in vitro systems is of limited use to inform questions relevant to translational medicine. In 2010 the field of Quantitative Systems Pharmacology (QSP) emerged via the publication of a white paper by Sorger et al. (Sorger et al. 2011). Quantitative Systems Pharmacology (QSP) models are multi-scale models that combine computational and experimental methods to elucidate, validate and apply new pharmacological concepts to the development of novel therapeutics. QSP models attempt to understand how biological function is disregulated in disease and how to best use this knowledge to develop new treatments. The discipline is a result of the convergence of the fields of Systems Biology, the science of pharmacokinetics (PK) and pharmacodynamics (PD). Multi-scale models link drug-target interaction kinetics to the subsequent
cellular response in the context of animal or human (disease) physiology as illustrated in Figure 1. PK/PD models have been used since the 1960s to guide dose and dosing schedule selection in the clinic (Csajka and Verotta 2006). These models have evolved from the use of empirical functions describing the observed PK/PD data to complex, multi-scale systems pharmacology models which reflect the essential underlying rules of biology, physiology and pharmacology enabled by modern numerical analysis and scientific computing to describe nonlinear behaviors.
Figure 1: Quantitative Systems Pharmacology (QSP) models are multi-scale models that link protein- or drug- interaction kinetics to the subsequent cellular response in the context of animal or human (disease) physiology. QSP models enable the translation of preclinical science into the clinic.
Multi-scale models are either fit for purpose and therefore highly question dependent or aspire to describe disease (Cook and Bies 2016). These multi-scale models link diverse data-sets mechanistically in the model, through the simulated interaction of disease relevant processes. This mechanistic linkage provides the most natural, intuitive interpretation of an integrated dataset and allows to ask broader scientific questions and bridge the gap between preclinical to clinical translation (Clegg and Mac Gabhann 2015). As a result all major pharmaceuticals have invested into Quantitative Systems
Pharmacology in the recent years (Helmlinger et al. 2017), (Milligan et al. 2013),(Dolgos et al. 2016),(Visser et al. 2014). Of major clinical interest is to predict the effect of patient variability and to computationally explore drug combinations. The impact of patient variability on treatment response can be assessed by simulating the response of a virtual patient cohort. With an ever larger number of targeted therapies approved, it is not clinically tractable to test all possible combinations. Therefore, there is an opportunity to combine multi-scale models and statistical models to address this complex question of predicting drug combinations in the clinic.
Examples of Successful Implementation and Application In the recent years multiple efforts have emerged to build large multi-scale models ranging from whole cell models of bacteria (Karr et al. 2012) to complex models of mammalian cells (Froehlich et al. 2018) and disease models (Musante et al. 2017). These models deal with events that happen on very different scales, in time and space, often requiring different modeling approaches to be combined. In the following, we discuss three applications of multi-scale models, increasing in size and complexity:
1. Cellular multi-scale models that link input-signals to phenotype With the increase in computational power, new computational tools and methods (Babtie and Stumpf 2017),(Lopez et al. 2013),(Tangherloni et al. 2017) more complex multi-scale models have been developed in the last decade ranging from bacterial whole cell models to models that represent more than one pathway in mammalian cells. Bacterial whole cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment. Karr et al have built a whole-cell computational model for the bacterium Mycoplasma genitalium (Karr et al. 2012), a human urogenital parasite whose genome contains 525 genes (Fraser et al. 1995). The model accurately predicts a wide range of observable cellular behaviors. Recently, more complex models linking biochemical reactions to phenotype of human cells type (cancer cell lines as well as primary cells) have been developed (Bouhaddou et al. 2018), (Berndt et al.
2018), (Froehlich et al. 2018). Berndt et al. developed a comprehensive model of rat hepatocytes (Berndt et al. 2018). The authors simulated temporal variations in the metabolic state of the liver over 24 hours in response to multiple perturbations. Bouhaddou et al. have developed a hybrid stochasticdeterministic cancer cell model that includes receptor tyrosine kinase signaling, cell cycle, DNA damage, gene expression that is predictive of the phenotypic responses for a non-transformed cell line MCF10A over a time-scale of 48 hours (Bouhaddou et al. 2018). The model with more than 600 biochemical reactions was used to predict apoptosis for the U87 glioma cell line, based on its mRNA expression profile. The model predictions were in good agreement with the experimental data and validated the model. Taking it one step further, Froehlich et al. have built one of the largest dynamic pathway models. The model describes major cancer-associated pathways accounting for 108 genes and 36 activating mutations yielding a total of 1,228 molecular species in 4 compartments resulting in 2,686 reactions and includes 7 tyrosine kinase inhibitors. The mechanistic model of signal transduction and drug actions is complemented by a simple model for relative cell viability. The model was parameterized with data from over 100 human cancer cell lines. To build and train such a large models a new computational framework was needed that allows training of mechanistic models at a previously infeasible scale (Froehlich et al. 2018). In order to estimate thousands for parameters from a large experimental data-set in less then a week a multi-start local optimization was used. To assess the uncertainty in the model the authors borrowed approaches commonly used in the machine learning community and performed a 5-fold crossvalidation with 5 pairs of training (80%; 96 cell lines) and test datasets (20%; 24 cell lines). The authors reduced computation time by using a sparse linear solver and a tailored variant of adjoint sensitivity analysis (Kaltenbacher, Theis, and Hasenauer 2017) as well as parallelization on the level of cell lines. In drug development smaller fit-for-purpose multi-scale models are applied to guide the clinical translation of single agent or combination therapies. Mathematical tumor growth inhibition models are probably the most established multi-scale models and allow the identification of drug-related and species-related parameters (Bernard et al. 2012). An example of a relatively simple multi-scale model is a tumor growth inhibition model of a c-Met- (Yamazaki et al. 2008) and a PI3K-inhibitor (Salphati et al.
2010). The models link drug plasma concentration to target inhibition in the tumor, to tumor growth inhibition. These models can be used to identify minimal drug thresholds in the plasma necessary to
achieve tumor stasis or regression. These multi-scale models can be applied to support the selection of pharmacodynamic biomarkers (target or downstream marker) and guide the human dose selection prior to the compound entering clinical development. 2. Multi-scale models to explore combination treatments and optimize dosing regimens In order to explore potential drug combinations with computational models, more complex, multi-scale models are needed (Kirouac et al. 2017), (Gadkar et al. 2014). These models need to include at a minimum the drugs of interest for the combination as well as a clinical relevant model output. Ideally, these models are based on pre-clinical and clinical data. The model by Gadkar et al. is a multi-scale model that includes statin and an anti-PCSK9 monoclonal antibody therapy to predict low density lipoprotein (LDL) changes to support clinical development. Mechanistic interactions and cross-regulation of circulating LDL cholesterol, LDL receptor, and PCSK9 are included. Numerous virtual subjects were simulated and validated against clinical data. A key application of the model was the exploration of LDL modulation for various dosing regimens of drug treatment to guide clinical trial design. The model by Kirouac et al. allows the systematic exploration of all possible two- and three-way drug combination targeting the epidermal growth factor receptor (EGFR) as well as all components of the mitogen-activated protein kinase (MAPK) cascade in colorectal cancer. The model predicts tumor growth inhibition in preclinical models as well as clinical trial outcome (Kirouac et al. 2017). The model is multiscale and quantitatively describes the signaling responses observed in cell lines as well as in vivo tumor growth inhibition in patient derived xenografts and reproduces available clinical data capturing changes in tumor size in response to EGFR, BRAF, and MEK inhibitors. The authors predicted the changes in tumor size for an ERK inhibitor based on the underlying biological and pharmacological variability. The model was used to computationally asses all 16 possible combinations of inhibitors targeting EGFR, BRAF, MEK and ERK. This is an elegant example how multi-scale models can help bridge the divide between preclinical data and clinical strategy and can provide a framework to support the prioritization of combinations.
3. Multi-scale models to understand disease progression Disease models are computational models that describe the worsening of disease as a function of time and incorporate longitudinal molecular and clinical data (Cook and Bies 2016). They can be used to explore therapeutic intervention. Regulatory agencies have embraced disease progression models as powerful tools that can be used to improve drug development productivity (Madrasi et al. 2018). In addition, cost-effectiveness analysis and genomic analysis are novel applications of disease models. The endocrine system lends itself to build multi-scale disease models. It is highly dynamic, with hormone levels exhibiting complex temporal dynamics. Dysregulation of these dynamic processes can lead to diseases like type 2 diabetes (T2D). Since 1960, numerous mathematical models have been developed to describe the glucose-insulin system, to analyze data from diagnostic tests and to quantify drug effects. Computational disease models of T2D range from phenomenological to semi-mechanistic to mechanistic systems biology models and have been summarized by Landersdorfer and Ajimera (Landersdorfer and Jusko 2008),(Ajmera et al. 2013). The appropriate model type depends highly upon the problem at hand. Whereas phenomenological models are well suited to answer questions that are relatively narrow in scope (e.g. dose selection) mechanistic multi-scale models enable the exploration of broader scientific questions. T2D is thought to result from the combination of two metabolic defects, insulin resistance and the failure of insulin secreting pancreatic beta-cells. Ha et al. developed a phenomenological model that describes the whole-body responses to insulin resistance including the upregulation of beta-cell function on short and medium timescales and changes of beta-cell mass over longer timescales (Ha, Satin, and Sherman 2016). The model predicts the effect of temporary weight changes as well as the impact of gastric bypass surgery but can not predict the impact of novel therapies like GLP-1 agonists. Roge et al. developed a semi-mechanistic model describing the release of GIP and GLP-1 after ingestion of various glucose doses in healthy volunteers and patients with T2D (Røge, Bagger, and Alsk 2017). By linking the model with an insulin secretion model, the model can help elucidate the important role of incretin hormones in glucose metabolism in healthy individuals and T2D patients and show that the secretion of the hormones is similar for healthy individuals and patients with T2D.
The largest and most detailed multi-scale T2D disease model is based on the Entelos Metabolism PhysioLab® platform (Entelos Holding Corp 2010). PhysioLab is a large-scale commercially available model to simulate human metabolism. The model includes the regulation of energy metabolism and storage in several major organ systems including liver, muscle, adipose, kidney, and intestine, as well as the regulation and effects of key hormones including insulin, glucagon, adiponectin, epinephrine, GLP-1, and GIP. Model analysis pointed to two mechanisms: as glucose concentrations are reduced there is less opportunity for further reductions since the effect of incretins are glucose dependent, and the combined efficacy is limited by the maximum capacity of the adenylate cyclase pathway. Simulation of a GLP-1/GIP dual agonist in a virtual patient cohort resulted in a modest reduction in HbA1C above the effect of the GLP-1 monotherapy. This result the informed a No-Go decision prior to lead selection and thus enabling the prioritization of other discovery stage programs with a higher probability of clinical success (Rieger and Musante 2016). Another complex disease that has attracted phenomenological and detailed disease models is Alzheimer’s disease including amyloid β aggregation and hyperphosphorylated tau proteins (Ahmed 2016; Petrella et al. 2019; Stepanov et al. 2018).
Challenges for multi-scale models: In order to address some of these challenges the Interagency Modeling and Analysis Group (IMAG) was formed in 2003. The IMAG Multiscale Modeling (MSM) Consortium contains today over 100 multiscale models and is actively addressing many pressing issues facing the multiscale modeling community (MSM Consortium). One of the key challenges of multi-scale models is the size and complexity of the models. We may need to use network inference to help identify the scope of the multi-scale models (Chasman, Siahpirani, and Roy 2016). Currently, the building and application of complex multi-scale models is regarded with skepticism – given the potential for human error in building the modes and the fact that many of the parameters are unknown. In order to build, refine, validate and utilize multi-scale models more readily, we must become better at sharing and annotating models, including the sharing of the experimental data and metadata that was
used to train the models. Some of these tools and standards are emerging (Wierling, Herwig, and Lehrach 2007). If continuously updated, shared and used by the community multi-scale models could serve as the current knowledge base of what is currently known about a cell, organ, organism or disease. .A number of published models can already be retrieved from a model repository like BioModels (Chelliah et al. 2015) and reused as submodels in multi-scale models. The latest release of BioModels broadened the scope of accepted models and allows the submission of models other than SBML (Systems Biology Markup Language) models. BioModels now offers a version-control backed environment in which authors and curators can work collaboratively (Glont et al. 2018). Ideally, large multi-scale models are developed like open source software. The curation of different data to constrain these multi-scale models is labor intensive since the data is often a mixture of internally generated and published data. New meta-databases that integrate data from individual databases similar to ConsensusPathDB (Kamburov et al. 2013) or summarize metabolic pathways (Kamburov et al. 2013) are emerging which simplify and accelerate model building and parameterization. Since it is impossible to measure all parameters directly, model calibration is crucial for the development of quantitative models. The unknown parameters are typically estimated by minimizing the mismatch between model prediction and measured data. Given the size and complexity of multi-scale models additional optimization techniques are needed – especially if different modeling techniques like agent-based models or deterministic models with events or logic operations are combined (Kamburov et al. 2013). Tools like INDRA (Integrated Network and Dynamical Reasoning Assembler) Interactive Pathway Map (INDRA-IPM), a web-based pathway modeling tool could transform how we build multi-scale disease models. INDRA-IPM allows the user to construct and edit pathway maps in natural language, to display the results in familiar graphical formats and export models in several different standard exchange formats like models as SBML, SBGN, BNGL, Kappa, PySB and CX (Todorov et al. 2019).
One of the key questions for large multi-scale models is how to establish model credibility. Consistent criteria for model of verification and validation (V&V) of multi-scale models are lacking
(Kirouac 2018) especially if these models will be used to guide regulatory decisions. Verification is the process of determining that a model implementation accurately represents the modeler’s conceptual description of the model. Validation is the process of determining the degree to which a model is an accurate representation of the biological or clinical data from the perspective of the intended uses of the model. Depending on the question of interest and the decision consequence different levels of model uncertainty might be acceptable and risk metrics could be applied. Thus if these large multi-scale models are used to guide clinical decision making the establishment of standards similar to other engineering disciplines where computational models are used to make predictions will be necessary (Olsen and Raunak 2019).
Conclusion A major advantage of multi-scale models is that they link diverse data-sets mechanistically, through the simulated interaction of disease relevant processes. This mechanistic linkage provides the most natural, intuitive interpretation of an integrated dataset and allows to ask broad scientific questions. Depending on the question minimalistic fit-for-purpose and very detailed models including all of the mechanistic details should be considered. We see a great potential for multi-scale and Quantitative Systems Pharmacology models to improve the preclinical-to-clinical translation, because physical processes are represented. In the future multi-scale models could be combined with semi-supervised learning frameworks that translate experimentally derived mouse biological associations to the human in vivo disease context (Brubaker et al. 2019). Multi-scale models allow basic science to be translated into the clinic and represent an important tool to advance translational medicine by enabling forward and reverse translation. As we gain confidence in the ability of computational models to predict human biological processes, they will help guide us through the complex landscape of disease, ultimately leading to more effective and reliable methods for disease diagnosis, risk stratification, and therapy.
References and recommended reading special interest (•)
outstanding interest (••)
special interest (•) Ali, M et al.: The authors carried out the first pan- cancer, multi-omics comparative analysis of the relative performance of two proteomic technologies, RPPA and MS, in terms of their accuracy for predicting the sensitivity of both FDA-approved chemotherapeutics and targeted therapies. The prediction performance for the MS data or the combined proteomics data was significantly improved with BEMKL method whereas SVM showed only a marginal improvement.
Babtie and Stumpf et al The authors discuss the relative weaknesses and promises of different approaches aimed at addressing the issue of estimating hundreds or thousands of unknown kinetic parameters in whole cell models.
Glont (2018): Introduction of the new infrastructure for the model repository BioModels. Available at http://www.ebi.ac.uk/biomodels. It allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment.
Hass H (2017): The authors developed a ODE-base computational model that includes multiple receptor tyrosine kinase signaling pathways and show that training the bagged decision tree (BDT) model on features derived from the computational model improved the prediction of cell proliferation significantly compared to control
Madrasi (2018): Important concepts of bone physiology, osteoporosis, treatment options, mathematical modeling of osteoporosis, and the use of these models by the pharmaceutical industry and the Food and Drug Administration are discussed.
Musante (2017): Discussion of the unique value of disease-scale “platform” QSP models that are amenable to reuse and repurposing to support diverse clinical decisions in ways distinct from other pharmacometrics strategies.
outstanding interest (••) Alkan O. et al (2018) The authors have presented a computational model that links the DNA damage response signaling to phenotypic cellular responses and incorporates multiple time scales. Using the computational model, the systematically investigated potentiating drug combinations in vitro and in vivo between DNA damage–inducing chemotherapy (SN38 and gemcitabine) and DNA damage signaling
modulators (CHK1,ATR, ATM and DNA_PK inhibitors).
Berndt (2018): HEPATOKIN is a kinetic model comprises the major cellular metabolic pathways of cellular carbohydrate, lipid, and amino acid metabolism of rat hepatocytes and contains key electrophysiological processes at the inner mitochondrial membrane, including the membrane transport of various ions, the mitochondrial membrane potential, and the generation and utilization of the proton- motive force.
Bouhaddou (2018) The authors present a mechanistic model describing the interactions between commonly mutated pan-cancer signaling pathways— receptor tyrosine kinases, Ras/RAF/ERK, PI3K/AKT, mTOR, cell cycle, DNA damage, and apoptosis. They developed methods for how to tailor the model to multi-omics data, devise a novel stochastic algorithm to induce non-genetic cell-to-cell fluctuations in mRNA and protein quantities over time, and train the model against a wealth of biochemical and cell fate data to gain insight into the systems-level, context-specific control of proliferation and death.
Froehlich F (2018); The authors have constructed a detailed, large-scale mechanistic model of cancerrelated signaling pathways . They developed a novel computational framework to speed up computation time over 30,000-fold. They demonstrate that pronounced parameter uncertainties do not imply pronounced prediction uncertainties.
Froehlich H (2018): Authors review the potential of state-of-the-art data science approaches for personalized medicine, discuss open challenges, and highlight directions that may help to overcome them in the future.
Brubaker (2019): The authors demonstrate that despite the intrinsic limitation murine disease models, their semi-supervised learning approach prospectively discovers mouse features predictive of human biology, offering a valuable tool for inter-species molecular translation.
Kirouac (2017): Step-wise description of the development of a mechanism- based model of the MAPK signaling network in BRAFV600-mutant CRC. The model links cellular biochemistry and genetics to in vitro cell growth, in vivo tumor kinetics in CDX and PDX models, and ultimately clinical tumor responses.
Todorov(2019): Introduction of INDRA-IPM (Interactive Pathway Map) a web-based pathway map modeling tool that combines natural language processing with automated model assembly and visualization. INDRA- IPM contextualizes models with expression data and exports them to standard format.
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S2452-3100(19)30035-6
DOI:
https://doi.org/10.1016/j.coisb.2019.10.019
Reference:
COISB 270
To appear in:
Current Opinion in Systems Biology
Received Date: 1 July 2019 Revised Date:
31 October 2019
Accepted Date: 31 October 2019
Please cite this article as: Schoeberl, B, Quantitative Systems Pharmacology Models as a Key to Translational Medicine, Current Opinion in Systems Biology, https://doi.org/10.1016/j.coisb.2019.10.019. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Quantitative Systems Pharmacology Models as a Key to Translational Medicine Birgit Schoeberl Novartis Institutes of Biomedical Research, 220 Massachusetts Ave. Cambridge MA 02139 [email protected]
Highlights: •
Quantitative Systems Pharmacology models are multi-scale with respect to time, space and species and a foundation of translational medicine.
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The complexity of multi-scale models is defined by the scientific question.
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Complex multi-scale models are regarded with skepticism based on the potential for human error and many unknown parameters.
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Opportunity for the community to address the challenges of multi-scale models: o
Develop tools to enable more efficient model building
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Improve model and data sharing,
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Develop best practices for model validation
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Advance computational frameworks to enable large scale parameter optimization
Abstract Recent advances in experimentation and computation have allowed us to build multi-scale models of unprecedented scale. Quantitative Systems Pharmacology (QSP) models are multi-scale models that link protein- or drug- interaction kinetics to cellular response in the context of animal or human (disease) physiology. One of the areas where QSP models hold the most promise, is in translating preclinical science into the clinic. In the following, I discuss recent examples of multi-scale models such as bacterial whole cell models, multi-scale tumor growth inhibition models to assess possible drug combinations and human disease models. Challenges of multi-scale models and emerging solutions will be discussed.
Introduction Knowing the biological building blocks is not sufficient for understanding health and disease. Biological function does not exclusively originate at the level of the gene but is determined by positive and negative feedback regulations between gene, RNA, protein and external cues. This inherent complexity necessitates the development of mathematical models that bridge different scales (time, molecules to organisms and across species). These models incorporate prior knowledge and are based on very diverse sets of experimental data. Advances in both high-throughput experimentation and computational power have opened up the possibility of creating and analyzing more complex dynamic models of biological systems (Hasenauer et al. 2015). Statistical and machine learning methods represent accessible options to analyze large scale data-sets. Statistical approaches are at the forefront of predicting drug sensitivity by linking genomic and proteomic information to drug sensitivity (Ali et al. 2018), (Li, Shi, and Liang 2019), (Niz et al. 2016). However, machine learning models are limited in their ability to extrapolate predictions into untrained regimes, to make longitudinal predictions or to explain causality. More generally, they still face challenges in their clinical applicability (Fröhlich et al. 2018). The field of Systems Biology developed in the early 2000s as a framework for assembling models of biological systems from systematic measurements (Chuang, Hofree, and Ideker 2010). Systems Biology models often focus on the understanding of how cells translate external signals into (phenotypic) responses (Alkan et al. 2018),(Hass et al. 2017),(Ryu et al. 2015). However, Systems Biology with its focus on in vitro systems is of limited use to inform questions relevant to translational medicine. In 2010 the field of Quantitative Systems Pharmacology (QSP) emerged via the publication of a white paper by Sorger et al. (Sorger et al. 2011). Quantitative Systems Pharmacology (QSP) models are multi-scale models that combine computational and experimental methods to elucidate, validate and apply new pharmacological concepts to the development of novel therapeutics. QSP models attempt to understand how biological function is disregulated in disease and how to best use this knowledge to develop new treatments. The discipline is a result of the convergence of the fields of Systems Biology, the science of pharmacokinetics (PK) and pharmacodynamics (PD). Multi-scale models link drug-target interaction kinetics to the subsequent
cellular response in the context of animal or human (disease) physiology as illustrated in Figure 1. PK/PD models have been used since the 1960s to guide dose and dosing schedule selection in the clinic (Csajka and Verotta 2006). These models have evolved from the use of empirical functions describing the observed PK/PD data to complex, multi-scale systems pharmacology models which reflect the essential underlying rules of biology, physiology and pharmacology enabled by modern numerical analysis and scientific computing to describe nonlinear behaviors.
Figure 1: Quantitative Systems Pharmacology (QSP) models are multi-scale models that link protein- or drug- interaction kinetics to the subsequent cellular response in the context of animal or human (disease) physiology. QSP models enable the translation of preclinical science into the clinic.
Multi-scale models are either fit for purpose and therefore highly question dependent or aspire to describe disease (Cook and Bies 2016). These multi-scale models link diverse data-sets mechanistically in the model, through the simulated interaction of disease relevant processes. This mechanistic linkage provides the most natural, intuitive interpretation of an integrated dataset and allows to ask broader scientific questions and bridge the gap between preclinical to clinical translation (Clegg and Mac Gabhann 2015). As a result all major pharmaceuticals have invested into Quantitative Systems
Pharmacology in the recent years (Helmlinger et al. 2017), (Milligan et al. 2013),(Dolgos et al. 2016),(Visser et al. 2014). Of major clinical interest is to predict the effect of patient variability and to computationally explore drug combinations. The impact of patient variability on treatment response can be assessed by simulating the response of a virtual patient cohort. With an ever larger number of targeted therapies approved, it is not clinically tractable to test all possible combinations. Therefore, there is an opportunity to combine multi-scale models and statistical models to address this complex question of predicting drug combinations in the clinic.
Examples of Successful Implementation and Application In the recent years multiple efforts have emerged to build large multi-scale models ranging from whole cell models of bacteria (Karr et al. 2012) to complex models of mammalian cells (Froehlich et al. 2018) and disease models (Musante et al. 2017). These models deal with events that happen on very different scales, in time and space, often requiring different modeling approaches to be combined. In the following, we discuss three applications of multi-scale models, increasing in size and complexity:
1. Cellular multi-scale models that link input-signals to phenotype With the increase in computational power, new computational tools and methods (Babtie and Stumpf 2017),(Lopez et al. 2013),(Tangherloni et al. 2017) more complex multi-scale models have been developed in the last decade ranging from bacterial whole cell models to models that represent more than one pathway in mammalian cells. Bacterial whole cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment. Karr et al have built a whole-cell computational model for the bacterium Mycoplasma genitalium (Karr et al. 2012), a human urogenital parasite whose genome contains 525 genes (Fraser et al. 1995). The model accurately predicts a wide range of observable cellular behaviors. Recently, more complex models linking biochemical reactions to phenotype of human cells type (cancer cell lines as well as primary cells) have been developed (Bouhaddou et al. 2018), (Berndt et al.
2018), (Froehlich et al. 2018). Berndt et al. developed a comprehensive model of rat hepatocytes (Berndt et al. 2018). The authors simulated temporal variations in the metabolic state of the liver over 24 hours in response to multiple perturbations. Bouhaddou et al. have developed a hybrid stochasticdeterministic cancer cell model that includes receptor tyrosine kinase signaling, cell cycle, DNA damage, gene expression that is predictive of the phenotypic responses for a non-transformed cell line MCF10A over a time-scale of 48 hours (Bouhaddou et al. 2018). The model with more than 600 biochemical reactions was used to predict apoptosis for the U87 glioma cell line, based on its mRNA expression profile. The model predictions were in good agreement with the experimental data and validated the model. Taking it one step further, Froehlich et al. have built one of the largest dynamic pathway models. The model describes major cancer-associated pathways accounting for 108 genes and 36 activating mutations yielding a total of 1,228 molecular species in 4 compartments resulting in 2,686 reactions and includes 7 tyrosine kinase inhibitors. The mechanistic model of signal transduction and drug actions is complemented by a simple model for relative cell viability. The model was parameterized with data from over 100 human cancer cell lines. To build and train such a large models a new computational framework was needed that allows training of mechanistic models at a previously infeasible scale (Froehlich et al. 2018). In order to estimate thousands for parameters from a large experimental data-set in less then a week a multi-start local optimization was used. To assess the uncertainty in the model the authors borrowed approaches commonly used in the machine learning community and performed a 5-fold crossvalidation with 5 pairs of training (80%; 96 cell lines) and test datasets (20%; 24 cell lines). The authors reduced computation time by using a sparse linear solver and a tailored variant of adjoint sensitivity analysis (Kaltenbacher, Theis, and Hasenauer 2017) as well as parallelization on the level of cell lines. In drug development smaller fit-for-purpose multi-scale models are applied to guide the clinical translation of single agent or combination therapies. Mathematical tumor growth inhibition models are probably the most established multi-scale models and allow the identification of drug-related and species-related parameters (Bernard et al. 2012). An example of a relatively simple multi-scale model is a tumor growth inhibition model of a c-Met- (Yamazaki et al. 2008) and a PI3K-inhibitor (Salphati et al.
2010). The models link drug plasma concentration to target inhibition in the tumor, to tumor growth inhibition. These models can be used to identify minimal drug thresholds in the plasma necessary to
achieve tumor stasis or regression. These multi-scale models can be applied to support the selection of pharmacodynamic biomarkers (target or downstream marker) and guide the human dose selection prior to the compound entering clinical development. 2. Multi-scale models to explore combination treatments and optimize dosing regimens In order to explore potential drug combinations with computational models, more complex, multi-scale models are needed (Kirouac et al. 2017), (Gadkar et al. 2014). These models need to include at a minimum the drugs of interest for the combination as well as a clinical relevant model output. Ideally, these models are based on pre-clinical and clinical data. The model by Gadkar et al. is a multi-scale model that includes statin and an anti-PCSK9 monoclonal antibody therapy to predict low density lipoprotein (LDL) changes to support clinical development. Mechanistic interactions and cross-regulation of circulating LDL cholesterol, LDL receptor, and PCSK9 are included. Numerous virtual subjects were simulated and validated against clinical data. A key application of the model was the exploration of LDL modulation for various dosing regimens of drug treatment to guide clinical trial design. The model by Kirouac et al. allows the systematic exploration of all possible two- and three-way drug combination targeting the epidermal growth factor receptor (EGFR) as well as all components of the mitogen-activated protein kinase (MAPK) cascade in colorectal cancer. The model predicts tumor growth inhibition in preclinical models as well as clinical trial outcome (Kirouac et al. 2017). The model is multiscale and quantitatively describes the signaling responses observed in cell lines as well as in vivo tumor growth inhibition in patient derived xenografts and reproduces available clinical data capturing changes in tumor size in response to EGFR, BRAF, and MEK inhibitors. The authors predicted the changes in tumor size for an ERK inhibitor based on the underlying biological and pharmacological variability. The model was used to computationally asses all 16 possible combinations of inhibitors targeting EGFR, BRAF, MEK and ERK. This is an elegant example how multi-scale models can help bridge the divide between preclinical data and clinical strategy and can provide a framework to support the prioritization of combinations.
3. Multi-scale models to understand disease progression Disease models are computational models that describe the worsening of disease as a function of time and incorporate longitudinal molecular and clinical data (Cook and Bies 2016). They can be used to explore therapeutic intervention. Regulatory agencies have embraced disease progression models as powerful tools that can be used to improve drug development productivity (Madrasi et al. 2018). In addition, cost-effectiveness analysis and genomic analysis are novel applications of disease models. The endocrine system lends itself to build multi-scale disease models. It is highly dynamic, with hormone levels exhibiting complex temporal dynamics. Dysregulation of these dynamic processes can lead to diseases like type 2 diabetes (T2D). Since 1960, numerous mathematical models have been developed to describe the glucose-insulin system, to analyze data from diagnostic tests and to quantify drug effects. Computational disease models of T2D range from phenomenological to semi-mechanistic to mechanistic systems biology models and have been summarized by Landersdorfer and Ajimera (Landersdorfer and Jusko 2008),(Ajmera et al. 2013). The appropriate model type depends highly upon the problem at hand. Whereas phenomenological models are well suited to answer questions that are relatively narrow in scope (e.g. dose selection) mechanistic multi-scale models enable the exploration of broader scientific questions. T2D is thought to result from the combination of two metabolic defects, insulin resistance and the failure of insulin secreting pancreatic beta-cells. Ha et al. developed a phenomenological model that describes the whole-body responses to insulin resistance including the upregulation of beta-cell function on short and medium timescales and changes of beta-cell mass over longer timescales (Ha, Satin, and Sherman 2016). The model predicts the effect of temporary weight changes as well as the impact of gastric bypass surgery but can not predict the impact of novel therapies like GLP-1 agonists. Roge et al. developed a semi-mechanistic model describing the release of GIP and GLP-1 after ingestion of various glucose doses in healthy volunteers and patients with T2D (Røge, Bagger, and Alsk 2017). By linking the model with an insulin secretion model, the model can help elucidate the important role of incretin hormones in glucose metabolism in healthy individuals and T2D patients and show that the secretion of the hormones is similar for healthy individuals and patients with T2D.
The largest and most detailed multi-scale T2D disease model is based on the Entelos Metabolism PhysioLab® platform (Entelos Holding Corp 2010). PhysioLab is a large-scale commercially available model to simulate human metabolism. The model includes the regulation of energy metabolism and storage in several major organ systems including liver, muscle, adipose, kidney, and intestine, as well as the regulation and effects of key hormones including insulin, glucagon, adiponectin, epinephrine, GLP-1, and GIP. Model analysis pointed to two mechanisms: as glucose concentrations are reduced there is less opportunity for further reductions since the effect of incretins are glucose dependent, and the combined efficacy is limited by the maximum capacity of the adenylate cyclase pathway. Simulation of a GLP-1/GIP dual agonist in a virtual patient cohort resulted in a modest reduction in HbA1C above the effect of the GLP-1 monotherapy. This result the informed a No-Go decision prior to lead selection and thus enabling the prioritization of other discovery stage programs with a higher probability of clinical success (Rieger and Musante 2016). Another complex disease that has attracted phenomenological and detailed disease models is Alzheimer’s disease including amyloid β aggregation and hyperphosphorylated tau proteins (Ahmed 2016; Petrella et al. 2019; Stepanov et al. 2018).
Challenges for multi-scale models: In order to address some of these challenges the Interagency Modeling and Analysis Group (IMAG) was formed in 2003. The IMAG Multiscale Modeling (MSM) Consortium contains today over 100 multiscale models and is actively addressing many pressing issues facing the multiscale modeling community (MSM Consortium). One of the key challenges of multi-scale models is the size and complexity of the models. We may need to use network inference to help identify the scope of the multi-scale models (Chasman, Siahpirani, and Roy 2016). Currently, the building and application of complex multi-scale models is regarded with skepticism – given the potential for human error in building the modes and the fact that many of the parameters are unknown. In order to build, refine, validate and utilize multi-scale models more readily, we must become better at sharing and annotating models, including the sharing of the experimental data and metadata that was
used to train the models. Some of these tools and standards are emerging (Wierling, Herwig, and Lehrach 2007). If continuously updated, shared and used by the community multi-scale models could serve as the current knowledge base of what is currently known about a cell, organ, organism or disease. .A number of published models can already be retrieved from a model repository like BioModels (Chelliah et al. 2015) and reused as submodels in multi-scale models. The latest release of BioModels broadened the scope of accepted models and allows the submission of models other than SBML (Systems Biology Markup Language) models. BioModels now offers a version-control backed environment in which authors and curators can work collaboratively (Glont et al. 2018). Ideally, large multi-scale models are developed like open source software. The curation of different data to constrain these multi-scale models is labor intensive since the data is often a mixture of internally generated and published data. New meta-databases that integrate data from individual databases similar to ConsensusPathDB (Kamburov et al. 2013) or summarize metabolic pathways (Kamburov et al. 2013) are emerging which simplify and accelerate model building and parameterization. Since it is impossible to measure all parameters directly, model calibration is crucial for the development of quantitative models. The unknown parameters are typically estimated by minimizing the mismatch between model prediction and measured data. Given the size and complexity of multi-scale models additional optimization techniques are needed – especially if different modeling techniques like agent-based models or deterministic models with events or logic operations are combined (Kamburov et al. 2013). Tools like INDRA (Integrated Network and Dynamical Reasoning Assembler) Interactive Pathway Map (INDRA-IPM), a web-based pathway modeling tool could transform how we build multi-scale disease models. INDRA-IPM allows the user to construct and edit pathway maps in natural language, to display the results in familiar graphical formats and export models in several different standard exchange formats like models as SBML, SBGN, BNGL, Kappa, PySB and CX (Todorov et al. 2019).
One of the key questions for large multi-scale models is how to establish model credibility. Consistent criteria for model of verification and validation (V&V) of multi-scale models are lacking
(Kirouac 2018) especially if these models will be used to guide regulatory decisions. Verification is the process of determining that a model implementation accurately represents the modeler’s conceptual description of the model. Validation is the process of determining the degree to which a model is an accurate representation of the biological or clinical data from the perspective of the intended uses of the model. Depending on the question of interest and the decision consequence different levels of model uncertainty might be acceptable and risk metrics could be applied. Thus if these large multi-scale models are used to guide clinical decision making the establishment of standards similar to other engineering disciplines where computational models are used to make predictions will be necessary (Olsen and Raunak 2019).
Conclusion A major advantage of multi-scale models is that they link diverse data-sets mechanistically, through the simulated interaction of disease relevant processes. This mechanistic linkage provides the most natural, intuitive interpretation of an integrated dataset and allows to ask broad scientific questions. Depending on the question minimalistic fit-for-purpose and very detailed models including all of the mechanistic details should be considered. We see a great potential for multi-scale and Quantitative Systems Pharmacology models to improve the preclinical-to-clinical translation, because physical processes are represented. In the future multi-scale models could be combined with semi-supervised learning frameworks that translate experimentally derived mouse biological associations to the human in vivo disease context (Brubaker et al. 2019). Multi-scale models allow basic science to be translated into the clinic and represent an important tool to advance translational medicine by enabling forward and reverse translation. As we gain confidence in the ability of computational models to predict human biological processes, they will help guide us through the complex landscape of disease, ultimately leading to more effective and reliable methods for disease diagnosis, risk stratification, and therapy.
References and recommended reading special interest (•)
outstanding interest (••)
special interest (•) Ali, M et al.: The authors carried out the first pan- cancer, multi-omics comparative analysis of the relative performance of two proteomic technologies, RPPA and MS, in terms of their accuracy for predicting the sensitivity of both FDA-approved chemotherapeutics and targeted therapies. The prediction performance for the MS data or the combined proteomics data was significantly improved with BEMKL method whereas SVM showed only a marginal improvement.
Babtie and Stumpf et al The authors discuss the relative weaknesses and promises of different approaches aimed at addressing the issue of estimating hundreds or thousands of unknown kinetic parameters in whole cell models.
Glont (2018): Introduction of the new infrastructure for the model repository BioModels. Available at http://www.ebi.ac.uk/biomodels. It allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment.
Hass H (2017): The authors developed a ODE-base computational model that includes multiple receptor tyrosine kinase signaling pathways and show that training the bagged decision tree (BDT) model on features derived from the computational model improved the prediction of cell proliferation significantly compared to control
Madrasi (2018): Important concepts of bone physiology, osteoporosis, treatment options, mathematical modeling of osteoporosis, and the use of these models by the pharmaceutical industry and the Food and Drug Administration are discussed.
Musante (2017): Discussion of the unique value of disease-scale “platform” QSP models that are amenable to reuse and repurposing to support diverse clinical decisions in ways distinct from other pharmacometrics strategies.
outstanding interest (••) Alkan O. et al (2018) The authors have presented a computational model that links the DNA damage response signaling to phenotypic cellular responses and incorporates multiple time scales. Using the computational model, the systematically investigated potentiating drug combinations in vitro and in vivo between DNA damage–inducing chemotherapy (SN38 and gemcitabine) and DNA damage signaling
modulators (CHK1,ATR, ATM and DNA_PK inhibitors).
Berndt (2018): HEPATOKIN is a kinetic model comprises the major cellular metabolic pathways of cellular carbohydrate, lipid, and amino acid metabolism of rat hepatocytes and contains key electrophysiological processes at the inner mitochondrial membrane, including the membrane transport of various ions, the mitochondrial membrane potential, and the generation and utilization of the proton- motive force.
Bouhaddou (2018) The authors present a mechanistic model describing the interactions between commonly mutated pan-cancer signaling pathways— receptor tyrosine kinases, Ras/RAF/ERK, PI3K/AKT, mTOR, cell cycle, DNA damage, and apoptosis. They developed methods for how to tailor the model to multi-omics data, devise a novel stochastic algorithm to induce non-genetic cell-to-cell fluctuations in mRNA and protein quantities over time, and train the model against a wealth of biochemical and cell fate data to gain insight into the systems-level, context-specific control of proliferation and death.
Froehlich F (2018); The authors have constructed a detailed, large-scale mechanistic model of cancerrelated signaling pathways . They developed a novel computational framework to speed up computation time over 30,000-fold. They demonstrate that pronounced parameter uncertainties do not imply pronounced prediction uncertainties.
Froehlich H (2018): Authors review the potential of state-of-the-art data science approaches for personalized medicine, discuss open challenges, and highlight directions that may help to overcome them in the future.
Brubaker (2019): The authors demonstrate that despite the intrinsic limitation murine disease models, their semi-supervised learning approach prospectively discovers mouse features predictive of human biology, offering a valuable tool for inter-species molecular translation.
Kirouac (2017): Step-wise description of the development of a mechanism- based model of the MAPK signaling network in BRAFV600-mutant CRC. The model links cellular biochemistry and genetics to in vitro cell growth, in vivo tumor kinetics in CDX and PDX models, and ultimately clinical tumor responses.
Todorov(2019): Introduction of INDRA-IPM (Interactive Pathway Map) a web-based pathway map modeling tool that combines natural language processing with automated model assembly and visualization. INDRA- IPM contextualizes models with expression data and exports them to standard format.
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