Use of mechanistic models to integrate and analyze multiple proteomic datasets

A scalable, open-source implementation of a large-scale mechanistic model for single cell proliferation and death signaling

Mechanistic models of how single cells respond to different perturbations can help integrate disparate big data sets or predict response to varied drug combinations. However, the construction and simulation of such models have proved challenging. Here, we developed a python-based model creation and simulation pipeline that converts a few structured text files into an SBML standard and is high-performance- and cloud-computing ready. We applied this pipeline to our large-scale, mechanistic pan-cancer signaling model (named SPARCED) and demonstrate it by adding an IFNγ pathway submodel. We then investigated whether a putative crosstalk mechanism could be consistent with experimental observations from the LINCS MCF10A Data Cube that IFNγ acts as an anti-proliferative factor. The analyses suggested this observation can be explained by IFNγ-induced SOCS1 sequestering activated EGF receptors. This work forms a foundational recipe for increased mechanistic model-based data integration on a single-cell level, an important building block for clinically-predictive mechanistic models.

Validation Through Collaboration: Encouraging Team Efforts to Ensure Internal and External Validity of Computational Models of Biochemical Pathways

Computational modelling of biochemical reaction pathways is an increasingly important part of neuroscience research. In order to be useful, computational models need to be valid in two senses: First, they need to be consistent with experimental data and able to make testable predictions (external validity). Second, they need to be internally consistent and independently reproducible (internal validity). Here, we discuss both types of validity and provide a brief overview of tools and technologies used to ensure they are met. We also suggest the introduction of new collaborative technologies to ensure model validity: an incentivised experimental database for external validity and reproducibility audits for internal validity. Both rely on FAIR principles and on collaborative science practices.

New analysis pipeline for high-throughput domain-peptide affinity experiments improves SH2 interaction data

Protein domain interactions with short linear peptides, such as those of the Src homology 2 (SH2) domain with phosphotyrosine-containing peptide motifs (pTyr), are ubiquitous and important to many biochemical processes of the cell. The desire to map and quantify these interactions has resulted in the development of high-throughput (HTP) quantitative measurement techniques, such as microarray or fluorescence polarization assays. For example, in the last 15 years, experiments have progressed from measuring single interactions to covering 500,000 of the 5.5 million possible SH2-pTyr interactions in the human proteome. However, high variability in affinity measurements and disagreements about positive interactions between published data sets led us here to reevaluate the analysis methods and raw data of published SH2-pTyr HTP experiments. We identified several opportunities for improving the identification of positive and negative interactions and the accuracy of affinity measurements. We implemented model-fitting techniques that are more statistically appropriate for the nonlinear SH2-pTyr interaction data. We also developed a method to account for protein concentration errors due to impurities and degradation or protein inactivity and aggregation. Our revised analysis increases the reported affinity accuracy, reduces the false-negative rate, and increases the amount of useful data by adding reliable true-negative results. We demonstrate improvement in classification of binding versus nonbinding when using machine-learning techniques, suggesting improved coherence in the reanalyzed data sets. We present revised SH2-pTyr affinity results and propose a new analysis pipeline for future HTP measurements of domain-peptide interactions.

Multisite EGFR phosphorylation is regulated by adaptor protein abundances and dimer lifetimes

Differential epidermal growth factor receptor (EGFR) phosphorylation is thought to couple receptor activation to distinct signaling pathways. However, the molecular mechanisms responsible for biased signaling are unresolved due to a lack of insight into the phosphorylation patterns of full-length EGFR. We extended a single-molecule pull-down technique previously used to study protein-protein interactions to allow for robust measurement of receptor phosphorylation. We found that EGFR is predominantly phosphorylated at multiple sites, yet phosphorylation at specific tyrosines is variable and only a subset of receptors share phosphorylation at the same site, even with saturating ligand concentrations. We found distinct populations of receptors as soon as 1 min after ligand stimulation, indicating early diversification of function. To understand this heterogeneity, we developed a mathematical model. The model predicted that variations in phosphorylation are dependent on the abundances of signaling partners, while phosphorylation levels are dependent on dimer lifetimes. The predictions were confirmed in studies of cell lines with different expression levels of signaling partners, and in experiments comparing low- and high-affinity ligands and oncogenic EGFR mutants. These results reveal how ligand-regulated receptor dimerization dynamics and adaptor protein concentrations play critical roles in EGFR signaling.

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.

Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor

Receptor tyrosine kinases (RTKs) typically contain multiple autophosphorylation sites in their cytoplasmic domains. Once activated, these autophosphorylation sites can recruit downstream signaling proteins containing Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains, which recognize phosphotyrosine-containing short linear motifs (SLiMs). These domains and SLiMs have polyspecific or promiscuous binding activities. Thus, multiple signaling proteins may compete for binding to a common SLiM and vice versa. To investigate the effects of competition on RTK signaling, we used a rule-based modeling approach to develop and analyze models for ligand-induced recruitment of SH2/PTB domain-containing proteins to autophosphorylation sites in the insulin-like growth factor 1 (IGF1) receptor (IGF1R). Models were parameterized using published datasets reporting protein copy numbers and site-specific binding affinities. Simulations were facilitated by a novel application of model restructuration, to reduce redundancy in rule-derived equations. We compare predictions obtained via numerical simulation of the model to those obtained through simple prediction methods, such as through an analytical approximation, or ranking by copy number and/or K_D value, and find that the simple methods are unable to recapitulate the predictions of numerical simulations. We created 45 cell line-specific models that demonstrate how early events in IGF1R signaling depend on the protein abundance profile of a cell. Simulations, facilitated by model restructuration, identified pairs of IGF1R binding partners that are recruited in anti-correlated and correlated fashions, despite no inclusion of cooperativity in our models. This work shows that the outcome of competition depends on the physicochemical parameters that characterize pairwise interactions, as well as network properties, including network connectivity and the relative abundances of competitors.

Cells rely on networks of interacting biomolecules to sense and respond to environmental perturbations and signals. However, it is unclear how information is processed to generate appropriate and specific responses to signals, especially given that these networks tend to share many components. For example, receptors that detect distinct ligands and regulate distinct cellular activities commonly interact with overlapping sets of downstream signaling proteins. Here, to investigate the downstream signaling of a well-studied receptor tyrosine kinase (RTK), the insulin-like growth factor 1 (IGF1) receptor (IGF1R), we formulated and analyzed 45 cell line-specific mathematical models, which account for recruitment of 18 different binding partners to six sites of receptor autophosphorylation in IGF1R. The models were parameterized using available protein copy number and site-specific affinity measurements, and restructured to allow for network generation. We find that recruitment is influenced by the protein abundance profile of a cell, with different patterns of recruitment in different cell lines. Furthermore, in a given cell line, we find that pairs of IGF1R binding partners may be recruited in a correlated or anti-correlated fashion. We demonstrate that the simulations of the model have greater predictive power than protein copy number and/or binding affinity data, and that even a simple analytical model cannot reproduce the predicted recruitment ranking obtained via simulations. These findings represent testable predictions and indicate that the outputs of IGF1R signaling depend on cell line-specific properties in addition to the properties that are intrinsic to the biomolecules involved.

A Step-by-Step Guide to Using BioNetFit

BioNetFit is a software tool designed for solving parameter identification problems that arise in the development of rule-based models. It solves these problems through curve fitting (i.e., nonlinear regression). BioNetFit is compatible with deterministic and stochastic simulators that accept BioNetGen language (BNGL)-formatted files as inputs, such as those available within the BioNetGen framework. BioNetFit can be used on a laptop or stand-alone multicore workstation as well as on many Linux clusters, such as those that use the Slurm Workload Manager to schedule jobs. BioNetFit implements a metaheuristic population-based global optimization procedure, an evolutionary algorithm (EA), to minimize a user-defined objective function, such as a residual sum of squares (RSS) function. BioNetFit also implements a bootstrapping procedure for determining confidence intervals for parameter estimates. Here, we provide step-by-step instructions for using BioNetFit to estimate the values of parameters of a BNGL-encoded model and to define bootstrap confidence intervals. The process entails the use of several plain-text files, which are processed by BioNetFit and BioNetGen. In general, these files include (1) one or more EXP files, which each contains (experimental) data to be used in parameter identification/bootstrapping; (2) a BNGL file containing a model section, which defines a (rule-based) model, and an actions section, which defines simulation protocols that generate GDAT and/or SCAN files with model predictions corresponding to the data in the EXP file(s); and (3) a CONF file that configures the fitting/bootstrapping job and that defines algorithmic parameter settings.

Generalizing Gillespie's Direct Method to Enable Network-Free Simulations

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

A mechanistic pan-cancer pathway model informed by multi-omics data interprets stochastic cell fate responses to drugs and mitogens

Most cancer cells harbor multiple drivers whose epistasis and interactions with expression context clouds drug and drug combination sensitivity prediction. We constructed a mechanistic computational model that is context-tailored by omics data to capture regulation of stochastic proliferation and death by pan-cancer driver pathways. Simulations and experiments explore how the coordinated dynamics of RAF/MEK/ERK and PI-3K/AKT kinase activities in response to synergistic mitogen or drug combinations control cell fate in a specific cellular context. In this MCF10A cell context, simulations suggest that synergistic ERK and AKT inhibitor-induced death is likely mediated by BIM rather than BAD, which is supported by prior experimental studies. AKT dynamics explain S-phase entry synergy between EGF and insulin, but simulations suggest that stochastic ERK, and not AKT, dynamics seem to drive cell-to-cell proliferation variability, which in simulations is predictable from pre-stimulus fluctuations in C-Raf/B-Raf levels. Simulations suggest MEK alteration negligibly influences transformation, consistent with clinical data. Tailoring the model to an alternate cell expression and mutation context, a glioma cell line, allows prediction of increased sensitivity of cell death to AKT inhibition. Our model mechanistically interprets context-specific landscapes between driver pathways and cell fates, providing a framework for designing more rational cancer combination therapy.

Cancer is a complex and diverse disease. Two people with the same cancer type often respond differently to the same treatment. These differences are primarily driven by the fact that two type-matched tumors can possess distinct sets of mutations and gene expression profiles, provoking differential sensitivity to drugs. Over the past few decades, we have seen a shift away from more broadly cytotoxic drugs to more targeted molecules therapies; but how to match a patient with a specific drug or drug cocktail remains a difficult problem. Here, we build a mechanistic ordinary differential equation 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. We develop methods for how to tailor the model to multi-omics data from a specific biological context, 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. One day, we hope models of this kind could be tailored to patient-derived tumor mRNA sequencing data and used to prioritize patient-specific drug regimens.

How low can you go?

Extremely low numbers of active epidermal growth factor receptors are sufficient to drive tumor growth.

Protein abundance of AKT and ERK pathway components governs cell type-specific regulation of proliferation

Signaling through the AKT and ERK pathways controls cell proliferation. However, the integrated regulation of this multistep process, involving signal processing, cell growth and cell cycle progression, is poorly understood. Here, we study different hematopoietic cell types, in which AKT and ERK signaling is triggered by erythropoietin (Epo). Although these cell types share the molecular network topology for pro‐proliferative Epo signaling, they exhibit distinct proliferative responses. Iterating quantitative experiments and mathematical modeling, we identify two molecular sources for cell type‐specific proliferation. First, cell type‐specific protein abundance patterns cause differential signal flow along the AKT and ERK pathways. Second, downstream regulators of both pathways have differential effects on proliferation, suggesting that protein synthesis is rate‐limiting for faster cycling cells while slower cell cycles are controlled at the G1‐S progression. The integrated mathematical model of Epo‐driven proliferation explains cell type‐specific effects of targeted AKT and ERK inhibitors and faithfully predicts, based on the protein abundance, anti‐proliferative effects of inhibitors in primary human erythroid progenitor cells. Our findings suggest that the effectiveness of targeted cancer therapy might become predictable from protein abundance.

Conservation of protein abundance patterns reveals the regulatory architecture of the EGFR-MAPK pathway

Various genetic mutations associated with cancer are known to alter cell signaling, but it is not clear whether they dysregulate signaling pathways by altering the abundance of pathway proteins. Using a combination of RNA sequencing and ultrasensitive targeted proteomics, we defined the primary components-16 core proteins and 10 feedback regulators-of the epidermal growth factor receptor (EGFR)-mitogen-activated protein kinase (MAPK) pathway in normal human mammary epithelial cells and then quantified their absolute abundance across a panel of normal and breast cancer cell lines as well as fibroblasts. We found that core pathway proteins were present at very similar concentrations across all cell types, with a variance similar to that of proteins previously shown to display conserved abundances across species. In contrast, EGFR and transcriptionally controlled feedback regulators were present at highly variable concentrations. The absolute abundance of most core proteins was between 50,000 and 70,000 copies per cell, but the adaptors SOS1, SOS2, and GAB1 were found at far lower amounts (2000 to 5000 copies per cell). MAPK signaling showed saturation in all cells between 3000 and 10,000 occupied EGFRs, consistent with the idea that adaptors limit signaling. Our results suggest that the relative stoichiometry of core MAPK pathway proteins is very similar across different cell types, with cell-specific differences mostly restricted to variable amounts of feedback regulators and receptors. The low abundance of adaptors relative to EGFR could be responsible for previous observations that only a fraction of total cell surface EGFR is capable of rapid endocytosis, high-affinity binding, and mitogenic signaling.

Mathematics in modern immunology

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.