An empirical Bayesian approach for model-based inference of cellular signaling networks

An integrated modelling approach for targeted degradation: insights on optimization, data requirements and PKPD predictions from semi- or fully-mechanistic models and exact steady state solutions

The value of an integrated mathematical modelling approach for protein degraders which combines the benefits of traditional turnover models and fully mechanistic models is presented. Firstly, we show how exact solutions of the mechanistic models of monovalent and bivalent degraders can provide insight on the role of each system parameter in driving the pharmacological response. We show how on/off binding rates and degradation rates are related to potency and maximal effect of monovalent degraders, and how such relationship can be used to suggest a compound optimization strategy. Even convoluted exact steady state solutions for bivalent degraders provide insight on the type of observations required to ensure the predictive capacity of a mechanistic approach. Specifically for PROTACs, the structure of the exact steady state solution suggests that the total remaining target at steady state, which is easily accessible experimentally, is insufficient to reconstruct the state of the whole system at equilibrium and observations on different species (such as binary/ternary complexes) are necessary. Secondly, global sensitivity analysis of fully mechanistic models for PROTACs suggests that both target and ligase baselines (actually, their ratio) are the major sources of variability in the response of non-cooperative systems, which speaks to the importance of characterizing their distribution in the target patient population. Finally, we propose a pragmatic modelling approach which incorporates the insights generated with fully mechanistic models into simpler turnover models to improve their predictive ability, hence enabling acceleration of drug discovery programs and increased probability of success in the clinic.

Bayesian parameter estimation for dynamical models in systems biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

Integrative modeling of the cell

A whole-cell model represents certain aspects of the cell structure and/or function. Due to the high complexity of the cell, an integrative modeling approach is often taken to utilize all available information including experimental data, prior knowledge and prior models. In this review, we summarize an emerging workflow of whole-cell modeling into five steps: (i) gather information; (ii) represent the modeled system into modules; (iii) translate input information into scoring function; (iv) sample the whole-cell model; (v) validate and interpret the model. In particular, we propose the integrative modeling of the cell by combining available (whole-cell) models to maximize the accuracy, precision, and completeness. In addition, we list quantitative predictions of various aspects of cell biology from existing whole-cell models. Moreover, we discuss the remaining challenges and future directions, and highlight the opportunity to establish an integrative spatiotemporal multi-scale whole-cell model based on a community approach.

Bayesian modeling reveals metabolite-dependent ultrasensitivity in the cyanobacterial circadian clock

Mathematical models can enable a predictive understanding of mechanism in cell biology by quantitatively describing complex networks of interactions, but such models are often poorly constrained by available data. Owing to its relative biochemical simplicity, the core circadian oscillator in Synechococcus elongatus has become a prototypical system for studying how collective dynamics emerge from molecular interactions. The oscillator consists of only three proteins, KaiA, KaiB, and KaiC, and near-24-h cycles of KaiC phosphorylation can be reconstituted in vitro. Here, we formulate a molecularly detailed but mechanistically naive model of the KaiA-KaiC subsystem and fit it directly to experimental data within a Bayesian parameter estimation framework. Analysis of the fits consistently reveals an ultrasensitive response for KaiC phosphorylation as a function of KaiA concentration, which we confirm experimentally. This ultrasensitivity primarily results from the differential affinity of KaiA for competing nucleotide-bound states of KaiC. We argue that the ultrasensitive stimulus-response relation likely plays an important role in metabolic compensation by suppressing premature phosphorylation at nighttime.

Bayesian inference using qualitative observations of underlying continuous variables

MOTIVATION

Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization.

RESULTS

We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling.

AVAILABILITY AND IMPLEMENTATION

The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Parallel Tempering with Lasso for model reduction in systems biology

Systems Biology models reveal relationships between signaling inputs and observable molecular or cellular behaviors. The complexity of these models, however, often obscures key elements that regulate emergent properties. We use a Bayesian model reduction approach that combines Parallel Tempering with Lasso regularization to identify minimal subsets of reactions in a signaling network that are sufficient to reproduce experimentally observed data. The Bayesian approach finds distinct reduced models that fit data equivalently. A variant of this approach that uses Lasso to perform selection at the level of reaction modules is applied to the NF-κB signaling network to test the necessity of feedback loops for responses to pulsatile and continuous pathway stimulation. Taken together, our results demonstrate that Bayesian parameter estimation combined with regularization can isolate and reveal core motifs sufficient to explain data from complex signaling systems.

Cells respond to diverse environmental cues using complex networks of interacting proteins and other biomolecules. Mathematical and computational models have become invaluable tools to understand these networks and make informed predictions to rationally perturb cell behavior. However, the complexity of detailed models that try to capture all known biochemical elements of signaling networks often makes it difficult to determine the key regulatory elements that are responsible for specific cell behaviors. Here, we present a Bayesian computational approach, PTLasso, to automatically extract minimal subsets of detailed models that are sufficient to explain experimental data. The method simultaneously calibrates and reduces models, and the Bayesian approach samples globally, allowing us to find alternate mechanistic explanations for the data if present. We demonstrate the method on both synthetic and real biological data and show that PTLasso is an effective method to isolate distinct parts of a larger signaling model that are sufficient for specific data.

PyDREAM: high-dimensional parameter inference for biological models in python

Summary

Biological models contain many parameters whose values are difficult to measure directly via experimentation and therefore require calibration against experimental data. Markov chain Monte Carlo (MCMC) methods are suitable to estimate multivariate posterior model parameter distributions, but these methods may exhibit slow or premature convergence in high-dimensional search spaces. Here, we present PyDREAM, a Python implementation of the (Multiple-Try) Differential Evolution Adaptive Metropolis [DREAM_(ZS)] algorithm developed by Vrugt and ter Braak (2008) and Laloy and Vrugt (2012). PyDREAM achieves excellent performance for complex, parameter-rich models and takes full advantage of distributed computing resources, facilitating parameter inference and uncertainty estimation of CPU-intensive biological models.

Availability and implementation

PyDREAM is freely available under the GNU GPLv3 license from the Lopez lab GitHub repository at http://github.com/LoLab-VU/PyDREAM.

Supplementary information

Supplementary data are available at Bioinformatics online.

Inferring the Impact of Regulatory Mechanisms that Underpin CD8+ T Cell Control of B16 Tumor Growth In vivo Using Mechanistic Models and Simulation

A major barrier for broadening the efficacy of immunotherapies for cancer is identifying key mechanisms that limit the efficacy of tumor infiltrating lymphocytes. Yet, identifying these mechanisms using human samples and mouse models for cancer remains a challenge. While interactions between cancer and the immune system are dynamic and non-linear, identifying the relative roles that biological components play in regulating anti-tumor immunity commonly relies on human intuition alone, which can be limited by cognitive biases. To assist natural intuition, modeling and simulation play an emerging role in identifying therapeutic mechanisms. To illustrate the approach, we developed a multi-scale mechanistic model to describe the control of tumor growth by a primary response of CD8+ T cells against defined tumor antigens using the B16 C57Bl/6 mouse model for malignant melanoma. The mechanistic model was calibrated to data obtained following adenovirus-based immunization and validated to data obtained following adoptive transfer of transgenic CD8+ T cells. More importantly, we use simulation to test whether the postulated network topology, that is the modeled biological components and their associated interactions, is sufficient to capture the observed anti-tumor immune response. Given the available data, the simulation results also provided a statistical basis for quantifying the relative importance of different mechanisms that underpin CD8+ T cell control of B16F10 growth. By identifying conditions where the postulated network topology is incomplete, we illustrate how this approach can be used as part of an iterative design-build-test cycle to expand the predictive power of the model.

Construction of protein interaction network involved in lung adenocarcinomas using a novel algorithm

Studies that only assess differentially-expressed (DE) genes do not contain the information required to investigate the mechanisms of diseases. A complete knowledge of all the direct and indirect interactions between proteins may act as a significant benchmark in the process of forming a comprehensive description of cellular mechanisms and functions. The results of protein interaction network studies are often inconsistent and are based on various methods. In the present study, a combined network was constructed using selected gene pairs, following the conversion and combination of the scores of gene pairs that were obtained across multiple approaches by a novel algorithm. Samples from patients with and without lung adenocarcinoma were compared, and the RankProd package was used to identify DE genes. The empirical Bayesian (EB) meta-analysis approach, the search tool for the retrieval of interacting genes/proteins database (STRING), the weighted gene coexpression network analysis (WGCNA) package and the differentially-coexpressed genes and links package (DCGL) were used for network construction. A combined network was also constructed with a novel rank-based algorithm using a combined score. The topological features of the 5 networks were analyzed and compared. A total of 941 DE genes were screened. The topological analysis indicated that the gene interaction network constructed using the WGCNA method was more likely to produce a small-world property, which has a small average shortest path length and a large clustering coefficient, whereas the combined network was confirmed to be a scale-free network. Gene pairs that were identified using the novel combined method were mostly enriched in the cell cycle and p53 signaling pathway. The present study provided a novel perspective to the network-based analysis. Each method has advantages and disadvantages. Compared with single methods, the combined algorithm used in the present study may provide a novel method to analyze gene interactions, with increased credibility.

Simulation Study on Effects of Order and Step Size of Runge-Kutta Methods that Solve Contagious Disease and Tumor Models

Biological processes such as contagious disease spread patterns and tumor growth dynamics are modelled using a set of coupled differential equations. Experimental data is usually used to calibrate models so they can be used to make future predictions. In this study, numerical methods were implemented to approximate solutions to mathematical models that were not solvable analytically, such as a SARS model. More complex models such as a tumor growth model involve high-dimensional parameter spaces; efficient numerical simulation techniques were used to search for optimal or close-to-optimal parameter values in the equations. Runge-Kutta methods are a group of explicit and implicit numerical methods that effectively solve the ordinary differential equations in these models. Effects of the order and the step size of Runge-Kutta methods were studied in order to maximize the search accuracy and efficiency in parameter spaces of the models. Numerical simulation results showed that an order of four gave the best balance between truncation errors and the simulation speed for SIR, SARS, and tumormodels studied in the project. The optimal step size for differential equation solvers was found to be model-dependent.

A primer on Bayesian inference for biophysical systems

Bayesian inference is a powerful statistical paradigm that has gained popularity in many fields of science, but adoption has been somewhat slower in biophysics. Here, I provide an accessible tutorial on the use of Bayesian methods by focusing on example applications that will be familiar to biophysicists. I first discuss the goals of Bayesian inference and show simple examples of posterior inference using conjugate priors. I then describe Markov chain Monte Carlo sampling and, in particular, discuss Gibbs sampling and Metropolis random walk algorithms with reference to detailed examples. These Bayesian methods (with the aid of Markov chain Monte Carlo sampling) provide a generalizable way of rigorously addressing parameter inference and identifiability for arbitrarily complicated models.

Numerical Simulation of a Tumor Growth Dynamics Model Using Particle Swarm Optimization

Tumor cell growth models involve high-dimensional parameter spaces that require computationally tractable methods to solve. To address a proposed tumor growth dynamics mathematical model, an instance of the particle swarm optimization method was implemented to speed up the search process in the multi-dimensional parameter space to find optimal parameter values that fit experimental data from mice cancel cells. The fitness function, which measures the difference between calculated results and experimental data, was minimized in the numerical simulation process. The results and search efficiency of the particle swarm optimization method were compared to those from other evolutional methods such as genetic algorithms.

In silico model-based inference: an emerging approach for inverse problems in engineering better medicines

Identifying the network of biochemical interactions that underpin disease pathophysiology is a key hurdle in drug discovery. While many components involved in these biological processes are identified, how components organize differently in health and disease remains unclear. In chemical engineering, mechanistic modeling provides a quantitative framework to capture our understanding of a reactive system and test this knowledge against data. Here, we describe an emerging approach to test this knowledge against data that leverages concepts from probability, Bayesian statistics, and chemical kinetics by focusing on two related inverse problems. The first problem is to identify the causal structure of the reaction network, given uncertainty as to how the reactive components interact. The second problem is to identify the values of the model parameters, when a network is known a priori.

Interlocked positive and negative feedback network motifs regulate β-catenin activity in the adherens junction pathway

The integrity of epithelial tissue architecture is maintained through adherens junctions that are created through extracellular homotypic protein-protein interactions between cadherin molecules. Cadherins also provide an intracellular scaffold for the formation of a multiprotein complex that contains signaling proteins, including β-catenin. Environmental factors and controlled tissue reorganization disrupt adherens junctions by cleaving the extracellular binding domain and initiating a series of transcriptional events that aim to restore tissue homeostasis. However, it remains unclear how alterations in cell adhesion coordinate transcriptional events, including those mediated by β-catenin in this pathway. Here were used quantitative single-cell and population-level in vitro assays to quantify the endogenous pathway dynamics after the proteolytic disruption of the adherens junctions. Using prior knowledge of isolated elements of the overall network, we interpreted these data using in silico model-based inference to identify the topology of the regulatory network. Collectively the data suggest that the regulatory network contains interlocked network motifs consisting of a positive feedback loop, which is used to restore the integrity of adherens junctions, and a negative feedback loop, which is used to limit β-catenin-induced gene expression.

A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems

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We propose the dQSSA model as a novel way of modelling complex biological networks.

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No low enzyme concentration assumption, covering more biological settings.

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Reduces the number of parameters, which simplifies optimisation.

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dQSSA was validated both in silico and in vitro.

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Both biochemical and signalling pathways can be modelled accurately and simply.

Quasi steady-state enzyme kinetic models are increasingly used in systems modelling. The Michaelis Menten model is popular due to its reduced parameter dimensionality, but its low-enzyme and irreversibility assumption may not always be valid in the in vivo context. Whilst the total quasi-steady state assumption (tQSSA) model eliminates the reactant stationary assumptions, its mathematical complexity is increased. Here, we propose the differential quasi-steady state approximation (dQSSA) kinetic model, which expresses the differential equations as a linear algebraic equation. It eliminates the reactant stationary assumptions of the Michaelis Menten model without increasing model dimensionality. The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico. Additionally, the dQSSA was able to predict coenzyme inhibition in the reversible lactate dehydrogenase enzyme, which the Michaelis Menten model failed to do. Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems. This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics.

An in-silico model of lipoprotein metabolism and kinetics for the evaluation of targets and biomarkers in the reverse cholesterol transport pathway

High-density lipoprotein (HDL) is believed to play an important role in lowering cardiovascular disease (CVD) risk by mediating the process of reverse cholesterol transport (RCT). Via RCT, excess cholesterol from peripheral tissues is carried back to the liver and hence should lead to the reduction of atherosclerotic plaques. The recent failures of HDL-cholesterol (HDL-C) raising therapies have initiated a re-examination of the link between CVD risk and the rate of RCT, and have brought into question whether all target modulations that raise HDL-C would be atheroprotective. To help address these issues, a novel in-silico model has been built to incorporate modern concepts of HDL biology, including: the geometric structure of HDL linking the core radius with the number of ApoA-I molecules on it, and the regeneration of lipid-poor ApoA-I from spherical HDL due to remodeling processes. The ODE model has been calibrated using data from the literature and validated by simulating additional experiments not used in the calibration. Using a virtual population, we show that the model provides possible explanations for a number of well-known relationships in cholesterol metabolism, including the epidemiological relationship between HDL-C and CVD risk and the correlations between some HDL-related lipoprotein markers. In particular, the model has been used to explore two HDL-C raising target modulations, Cholesteryl Ester Transfer Protein (CETP) inhibition and ATP-binding cassette transporter member 1 (ABCA1) up-regulation. It predicts that while CETP inhibition would not result in an increased RCT rate, ABCA1 up-regulation should increase both HDL-C and RCT rate. Furthermore, the model predicts the two target modulations result in distinct changes in the lipoprotein measures. Finally, the model also allows for an evaluation of two candidate biomarkers for in-vivo whole-body ABCA1 activity: the absolute concentration and the % lipid-poor ApoA-I. These findings illustrate the potential utility of the model in drug development.

Optimal experiment design for model selection in biochemical networks

Background

Mathematical modeling is often used to formalize hypotheses on how a biochemical network operates by discriminating between competing models. Bayesian model selection offers a way to determine the amount of evidence that data provides to support one model over the other while favoring simple models. In practice, the amount of experimental data is often insufficient to make a clear distinction between competing models. Often one would like to perform a new experiment which would discriminate between competing hypotheses.

Results

We developed a novel method to perform Optimal Experiment Design to predict which experiments would most effectively allow model selection. A Bayesian approach is applied to infer model parameter distributions. These distributions are sampled and used to simulate from multivariate predictive densities. The method is based on a k-Nearest Neighbor estimate of the Jensen Shannon divergence between the multivariate predictive densities of competing models.

Conclusions

We show that the method successfully uses predictive differences to enable model selection by applying it to several test cases. Because the design criterion is based on predictive distributions, which can be computed for a wide range of model quantities, the approach is very flexible. The method reveals specific combinations of experiments which improve discriminability even in cases where data is scarce. The proposed approach can be used in conjunction with existing Bayesian methodologies where (approximate) posteriors have been determined, making use of relations that exist within the inferred posteriors.

Determination of parameter identifiability in nonlinear biophysical models: A Bayesian approach

A major goal of biophysics is to understand the physical mechanisms of biological molecules and systems. Mechanistic models are evaluated based on their ability to explain carefully controlled experiments. By fitting models to data, biophysical parameters that cannot be measured directly can be estimated from experimentation. However, it might be the case that many different combinations of model parameters can explain the observations equally well. In these cases, the model parameters are not identifiable: the experimentation has not provided sufficient constraining power to enable unique estimation of their true values. We demonstrate that this pitfall is present even in simple biophysical models. We investigate the underlying causes of parameter non-identifiability and discuss straightforward methods for determining when parameters of simple models can be inferred accurately. However, for models of even modest complexity, more general tools are required to diagnose parameter non-identifiability. We present a method based in Bayesian inference that can be used to establish the reliability of parameter estimates, as well as yield accurate quantification of parameter confidence.

Machines vs. ensembles: effective MAPK signaling through heterogeneous sets of protein complexes

Despite the importance of intracellular signaling networks, there is currently no consensus regarding the fundamental nature of the protein complexes such networks employ. One prominent view involves stable signaling machines with well-defined quaternary structures. The combinatorial complexity of signaling networks has led to an opposing perspective, namely that signaling proceeds via heterogeneous pleiomorphic ensembles of transient complexes. Since many hypotheses regarding network function rely on how we conceptualize signaling complexes, resolving this issue is a central problem in systems biology. Unfortunately, direct experimental characterization of these complexes has proven technologically difficult, while combinatorial complexity has prevented traditional modeling methods from approaching this question. Here we employ rule-based modeling, a technique that overcomes these limitations, to construct a model of the yeast pheromone signaling network. We found that this model exhibits significant ensemble character while generating reliable responses that match experimental observations. To contrast the ensemble behavior, we constructed a model that employs hierarchical assembly pathways to produce scaffold-based signaling machines. We found that this machine model could not replicate the experimentally observed combinatorial inhibition that arises when the scaffold is overexpressed. This finding provides evidence against the hierarchical assembly of machines in the pheromone signaling network and suggests that machines and ensembles may serve distinct purposes in vivo. In some cases, e.g. core enzymatic activities like protein synthesis and degradation, machines assembled via hierarchical energy landscapes may provide functional stability for the cell. In other cases, such as signaling, ensembles may represent a form of weak linkage, facilitating variation and plasticity in network evolution. The capacity of ensembles to signal effectively will ultimately shape how we conceptualize the function, evolution and engineering of signaling networks.

Intracellular signaling networks are central to a cell's ability to adapt to its environment. Developing the capacity to effectively manipulate such networks would have a wide range of applications, from cancer therapy to synthetic biology. This requires a thorough understanding of the mechanisms of signal transduction, particularly the kinds of protein complexes that are formed during transmission of extracellular information to the nucleus. Traditionally, signaling complexes have been largely perceived (albeit often implicitly) as machine-like structures. However, the number of molecular complexes that could theoretically be formed by complex signaling networks is astronomically large. This has led to the pleiomorphic ensemble hypothesis, which posits that diverse and rapidly changing sets of transient protein complexes can transmit and process information. Our goal was to use computational approaches, specifically rule-based modeling, to test these hypotheses. We constructed a model of the prototypical yeast mating pathway and found significant ensemble-like behavior. Our results thus demonstrated that ensembles can in fact transmit extracellular signals with minimal noise. Additionally, a comparison of this model with one tailored to generate machine-like complexes displayed notable phenotypic differences, revealing potential advantages for ensemble-like signaling. Our demonstration that ensembles can function effectively will have a significant impact on how we conceptualize signaling and other processes inside cells.

Parameter trajectory analysis to identify treatment effects of pharmacological interventions

The field of medical systems biology aims to advance understanding of molecular mechanisms that drive disease progression and to translate this knowledge into therapies to effectively treat diseases. A challenging task is the investigation of long-term effects of a (pharmacological) treatment, to establish its applicability and to identify potential side effects. We present a new modeling approach, called Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT), to analyze the long-term effects of a pharmacological intervention. A concept of time-dependent evolution of model parameters is introduced to study the dynamics of molecular adaptations. The progression of these adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages of the treatment. The trajectories provide insight in the affected underlying biological systems and identify the molecular events that should be studied in more detail to unravel the mechanistic basis of treatment outcome. Modulating effects caused by interactions with the proteome and transcriptome levels, which are often less well understood, can be captured by the time-dependent descriptions of the parameters. ADAPT was employed to identify metabolic adaptations induced upon pharmacological activation of the liver X receptor (LXR), a potential drug target to treat or prevent atherosclerosis. The trajectories were investigated to study the cascade of adaptations. This provided a counter-intuitive insight concerning the function of scavenger receptor class B1 (SR-B1), a receptor that facilitates the hepatic uptake of cholesterol. Although activation of LXR promotes cholesterol efflux and -excretion, our computational analysis showed that the hepatic capacity to clear cholesterol was reduced upon prolonged treatment. This prediction was confirmed experimentally by immunoblotting measurements of SR-B1 in hepatic membranes. Next to the identification of potential unwanted side effects, we demonstrate how ADAPT can be used to design new target interventions to prevent these.

A driving ambition of medical systems biology is to advance our understanding of molecular processes that drive the progression of complex diseases such as Type 2 Diabetes and cardiovascular disease. This insight is essential to enable the development of therapies to effectively treat diseases. A challenging task is to investigate the long-term effects of a treatment, in order to establish its applicability and to identify potential side effects. As such, there is a growing need for novel approaches to support this research. Here, we present a new computational approach to identify treatment effects. We make use of a computational model of the biological system. The model is used to describe the experimental data obtained during different stages of the treatment. To incorporate the long-term/progressive adaptations in the system, induced by changes in gene and protein expression, the model is iteratively updated. The approach was employed to identify metabolic adaptations induced by a potential anti-atherosclerotic and anti-diabetic drug target. Our approach identifies the molecular events that should be studied in more detail to establish the mechanistic basis of treatment outcome. New biological insight was obtained concerning the metabolism of cholesterol, which was in turn experimentally validated.

Exploring higher-order EGFR oligomerisation and phosphorylation--a combined experimental and theoretical approach

The epidermal growth factor receptor (EGFR) kinase is generally considered to be activated by either ligand-induced dimerisation or a ligand-induced conformational change within pre-formed dimers. Ligand-induced higher-order EGFR oligomerisation or clustering has been reported but it is not clear how EGFR oligomers, as distinct from EGFR dimers, influence signaling outputs. To address this question, we combined measures of receptor clustering (microscopy; image correlation spectroscopy) and phosphorylation (Western blots) with modelling of mass-action chemical kinetics. A stable BaF/3 cell-line that contains a high proportion (>90%) of inactive dimers of EGFR-eGFP but no secreted ligand and no other detectable ErbB receptors was used as the model cell system. EGF at concentrations of greater than 1 nM was found to cluster EGFR-eGFP dimers into higher-order complexes and cause parallel increases in EGFR phosphorylation. The kinetics of EGFR clustering and phosphorylation were both rapid, plateauing within 2 minutes after stimulation with 30 nM EGF. A rule-based model was formulated to interpret the data. This model took into account ligand binding, ligand-induced conformational changes in the cytosolic tail, monomer-dimer-trimer-tetramer transitions via ectodomain- and kinase-mediated interactions, and phosphorylation. The model predicts that cyclic EGFR tetramers are the predominant phosphorylated species, in which activated receptor dimers adopt a cyclic side-by-side orientation, and that receptor kinase activation is stabilised by the intramolecular interactions responsible for cyclic tetramerization.

Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws

True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.

Trajectory-oriented Bayesian experiment design versus Fisher A-optimal design: an in depth comparison study

Motivation: Experiment design strategies for biomedical models with the purpose of parameter estimation or model discrimination are in the focus of intense research. Experimental limitations such as sparse and noisy data result in unidentifiable parameters and render-related design tasks challenging problems. Often, the temporal resolution of data is a limiting factor and the amount of possible experimental interventions is finite. To address this issue, we propose a Bayesian experiment design algorithm to minimize the prediction uncertainty for a given set of experiments and compare it to traditional A-optimal design.

Results: In an in depth numerical study involving an ordinary differential equation model of the trans-Golgi network with 12 partly non-identifiable parameters, we minimized the prediction uncertainty efficiently for predefined scenarios. The introduced method results in twice the prediction precision as the same amount of A-optimal designed experiments while introducing a useful stopping criterion. The simulation intensity of the algorithm's major design step is thereby reasonably affordable. Besides smaller variances in the predicted trajectories compared with Fisher design, we could also achieve smaller parameter posterior distribution entropies, rendering this method superior to A-optimal Fisher design also in the parameter space.

Availability: Necessary software/toolbox information are available in the supplementary material. The project script including example data can be downloaded from http://www.ist.uni-stuttgart.de/%7eweber/BayesFisher2012.

Contact:patrick.weber@ist.uni-stuttgart.de

Supplementary Information:Supplementary data are available at Bioinformatics online.

Bayesian inference of the lung alveolar spatial model for the identification of alveolar mechanics associated with acute respiratory distress syndrome

Acute respiratory distress syndrome (ARDS) is acute lung failure secondary to severe systemic inflammation, resulting in a derangement of alveolar mechanics (i.e. the dynamic change in alveolar size and shape during tidal ventilation), leading to alveolar instability that can cause further damage to the pulmonary parenchyma. Mechanical ventilation is a mainstay in the treatment of ARDS, but may induce mechano-physical stresses on unstable alveoli, which can paradoxically propagate the cellular and molecular processes exacerbating ARDS pathology. This phenomenon is called ventilator induced lung injury (VILI), and plays a significant role in morbidity and mortality associated with ARDS. In order to identify optimal ventilation strategies to limit VILI and treat ARDS, it is necessary to understand the complex interplay between biological and physical mechanisms of VILI, first at the alveolar level, and then in aggregate at the whole-lung level. Since there is no current consensus about the underlying dynamics of alveolar mechanics, as an initial step we investigate the ventilatory dynamics of an alveolar sac (AS) with the lung alveolar spatial model (LASM), a 3D spatial biomechanical representation of the AS and its interaction with airflow pressure and the surface tension effects of pulmonary surfactant. We use the LASM to identify the mechanical ramifications of alveolar dynamics associated with ARDS. Using graphical processing unit parallel algorithms, we perform Bayesian inference on the model parameters using experimental data from rat lung under control and Tween-induced ARDS conditions. Our results provide two plausible models that recapitulate two fundamental hypotheses about volume change at the alveolar level: (1) increase in alveolar size through isotropic volume change, or (2) minimal change in AS radius with primary expansion of the mouth of the AS, with the implication that the majority of change in lung volume during the respiratory cycle occurs in the alveolar ducts. These two model solutions correspond to significantly different mechanical properties of the tissue, and we discuss the implications of these different properties and the requirements for new experimental data to discriminate between the hypotheses.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

An evolutionary perspective on anti-tumor immunity

The challenges associated with demonstrating a durable response using molecular-targeted therapies in cancer has sparked a renewed interest in viewing cancer from an evolutionary perspective. Evolutionary processes have three common traits: heterogeneity, dynamics, and a selective fitness landscape. Mutagens randomly alter the genome of host cells creating a population of cells that contain different somatic mutations. This genomic rearrangement perturbs cellular homeostasis through changing how cells interact with their tissue microenvironment. To counterbalance the ability of mutated cells to outcompete for limited resources, control structures are encoded within the cell and within the organ system, such as innate and adaptive immunity, to restore cellular homeostasis. These control structures shape the selective fitness landscape and determine whether a cell that harbors particular somatic mutations is retained or eliminated from a cell population. While next-generation sequencing has revealed the complexity and heterogeneity of oncogenic transformation, understanding the dynamics of oncogenesis and how cancer cells alter the selective fitness landscape remain unclear. In this technology review, we will summarize how recent advances in technology have impacted our understanding of these three attributes of cancer as an evolutionary process. In particular, we will focus on how advances in genome sequencing have enabled quantifying cellular heterogeneity, advances in computational power have enabled explicit testing of postulated intra- and intercellular control structures against the available data using simulation, and advances in proteomics have enabled identifying novel mechanisms of cellular cross-talk that cancer cells use to alter the fitness landscape.

Properties of cell death models calibrated and compared using Bayesian approaches

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass-action models of receptor-mediated cell death. The width of the individual parameter distributions is largely determined by non-identifiability but covariation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model-based predictions whereas ignoring it (e.g., by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (∼20-fold) for competing 'direct' and 'indirect' apoptosis models having different numbers of parameters. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single-cell data represent a generally useful and rigorous approach to discriminate between competing hypotheses in the face of parametric and topological uncertainty.

Understanding immunology via engineering design: the role of mathematical prototyping

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

A quantitative systems approach to identify paracrine mechanisms that locally suppress immune response to Interleukin-12 in the B16 melanoma model

Interleukin-12 (IL12) enhances anti-tumor immunity when delivered to the tumor microenvironment. However, local immunoregulatory elements dampen the efficacy of IL12. The identity of these local mechanisms used by tumors to suppress immunosurveillance represents a key knowledge gap for improving tumor immunotherapy. From a systems perspective, local suppression of anti-tumor immunity is a closed-loop system - where system response is determined by an unknown combination of external inputs and local cellular cross-talk. Here, we recreated this closed-loop system in vitro and combined quantitative high content assays, in silico model-based inference, and a proteomic workflow to identify the biochemical cues responsible for immunosuppression. Following an induction period, the B16 melanoma cell model, a transplantable model for spontaneous malignant melanoma, inhibited the response of a T helper cell model to IL12. This paracrine effect was not explained by induction of apoptosis or creation of a cytokine sink, despite both mechanisms present within the co-culture assay. Tumor-derived Wnt-inducible signaling protein-1 (WISP-1) was identified to exert paracrine action on immune cells by inhibiting their response to IL12. Moreover, WISP-1 was expressed in vivo following intradermal challenge with B16F10 cells and was inferred to be expressed at the tumor periphery. Collectively, the data suggest that (1) biochemical cues associated with epithelial-to-mesenchymal transition can shape anti-tumor immunity through paracrine action and (2) remnants of the immunoselective pressure associated with evolution in cancer include both sculpting of tumor antigens and expression of proteins that proactively shape anti-tumor immunity.

Quantifying crosstalk among interferon-γ, interleukin-12, and tumor necrosis factor signaling pathways within a TH1 cell model

T helper (T(H)) cells integrate biochemical cues present in the tissue microenvironment and produce cytokines that orchestrate immune responses. Previous discoveries have revealed a qualitative understanding of how T(H) cells process this biochemical information; however, the lack of methods to quantify how well these depictions apply to a particular cell type limits our ability to translate our knowledge of the immune response from one biological system to another. We used model-based inference methods and quantitative flow cytometric analysis in mouse T(H)1 cells to determine the relative contributions of different putative branches in the signaling network that responds to the cytokine interleukin-12 (IL-12), which links innate and adaptive immunity. The response of T(H)1 cells to IL-12 exhibited hysteresis because it depended on both current and past exposure and engaged a positive feedback mechanism through the direct activation of signal transducer and activator of transcription 1. The hysteresis in the dose-response curve to IL-12 created a transient "memory" by sustaining cytokine secretion after the withdrawal of the stimulus. In summary, this combined experimental and computational approach illustrates how model-based inference can be used to better understand how cells process and act upon biochemical cues present in the tissue microenvironment.

A Bayesian approach to targeted experiment design

Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity.

Results: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions.

Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html

Contact:j.vanlier@tue.nl; N.A.W.v.Riel@tue.nl

Supplementary information:Supplementary data are available at Bioinformatics online.

Age-corrected beta cell mass following onset of type 1 diabetes mellitus correlates with plasma C-peptide in humans

BACKGROUND

The inability to produce insulin endogenously precipitates the clinical symptoms of type 1 diabetes mellitus. However, the dynamic trajectory of beta cell destruction following onset remains unclear. Using model-based inference, the severity of beta cell destruction at onset decreases with age where, on average, a 40% reduction in beta cell mass was sufficient to precipitate clinical symptoms at 20 years of age. While plasma C-peptide provides a surrogate measure of endogenous insulin production post-onset, it is unclear as to whether plasma C-peptide represents changes in beta cell mass or beta cell function. The objective of this paper was to determine the relationship between beta cell mass and endogenous insulin production post-onset.

METHODS AND FINDINGS

Model-based inference was used to compare direct measures of beta cell mass in 102 patients against contemporary measures of plasma C-peptide obtained from three studies that collectively followed 834 patients post-onset of clinical symptoms. An empirical Bayesian approach was used to establish the level of confidence associated with the model prediction. Age-corrected estimates of beta cell mass that were inferred from a series of landmark pancreatic autopsy studies significantly correlate (p>0.9995) with contemporary measures of plasma C-peptide levels following onset.

CONCLUSIONS

Given the correlation between beta cell mass and plasma C-peptide following onset, plasma C-peptide may provide a surrogate measure of beta cell mass in humans. The clinical relevance of this study is that therapeutic strategies that provide an increase in plasma C-peptide over the predicted value for an individual may actually improve beta cell mass. The model predictions may establish a standard historical "control" group - a prior in a Bayesian context - for clinical trials.

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of interleukin-12 (IL-12) signaling in naïve CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo-equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.

Automated Bayesian model development for frequency detection in biological time series

Background

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies.

Results

In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing.

Conclusions

Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Identification of models of heterogeneous cell populations from population snapshot data

Background

Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations.

Results

In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed.

Conclusions

The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets.

Thermodynamically consistent Bayesian analysis of closed biochemical reaction systems

Background

Estimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.

Results

We introduce a Bayesian analysis approach for computing thermodynamically consistent estimates of the rate constants of a closed biochemical reaction system with known stoichiometry given experimental data. Our method employs an appropriately designed prior probability density function that effectively integrates fundamental biophysical and thermodynamic knowledge into the inference problem. Moreover, it takes into account experimental strategies for collecting informative observations of molecular concentrations through perturbations. The proposed method employs a maximization-expectation-maximization algorithm that provides thermodynamically feasible estimates of the rate constant values and computes appropriate measures of estimation accuracy. We demonstrate various aspects of the proposed method on synthetic data obtained by simulating a subset of a well-known model of the EGF/ERK signaling pathway, and examine its robustness under conditions that violate key assumptions. Software, coded in MATLAB^®, which implements all Bayesian analysis techniques discussed in this paper, is available free of charge at http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html.

Conclusions

Our approach provides an attractive statistical methodology for estimating thermodynamically feasible values for the rate constants of a biochemical reaction system from noisy time series observations of molecular concentrations obtained through perturbations. The proposed technique is theoretically sound and computationally feasible, but restricted to quantitative data obtained from closed biochemical reaction systems. This necessitates development of similar techniques for estimating the rate constants of open biochemical reaction systems, which are more realistic models of cellular function.

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales.

Classic and contemporary approaches to modeling biochemical reactions

Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and application of deterministic biochemical models, with particular emphasis on a simple enzyme-catalyzed reaction. Networks of coupled ordinary differential equations (ODEs) are the natural language for describing enzyme kinetics in a mass action approximation. We illustrate this point by showing how the familiar Briggs-Haldane formulation of Michaelis-Menten kinetics derives from the outer (or quasi-steady-state) solution of a dynamical system of ODEs describing a simple reaction under special conditions. We discuss how parameters in the Michaelis-Menten approximation and in the underlying ODE network can be estimated from experimental data, with a special emphasis on the origins of uncertainty. Finally, we extrapolate from a simple reaction to complex models of multiprotein biochemical networks. The concepts described in this review, hitherto of interest primarily to practitioners, are likely to become important for a much broader community of cellular and molecular biologists attempting to understand the promise and challenges of "systems biology" as applied to biochemical mechanisms.

Inferring predominant pathways in cellular models of breast cancer using limited sample proteomic profiling

Background

Molecularly targeted drugs inhibit aberrant signaling within oncogenic pathways. Identifying the predominant pathways at work within a tumor is a key step towards tailoring therapies to the patient. Clinical samples pose significant challenges for proteomic profiling, an attractive approach for identifying predominant pathways. The objective of this study was to determine if information obtained from a limited sample (i.e., a single gel replicate) can provide insight into the predominant pathways in two well-characterized breast cancer models.

Methods

A comparative proteomic analysis of total cell lysates was obtained from two cellular models of breast cancer, BT474 (HER2+/ER+) and SKBR3 (HER2+/ER-), using two-dimensional electrophoresis and MALDI-TOF mass spectrometry. Protein interaction networks and canonical pathways were extracted from the Ingenuity Pathway Knowledgebase (IPK) based on association with the observed pattern of differentially expressed proteins.

Results

Of the 304 spots that were picked, 167 protein spots were identified. A threshold of 1.5-fold was used to select 62 proteins used in the analysis. IPK analysis suggested that metabolic pathways were highly associated with protein expression in SKBR3 cells while cell motility pathways were highly associated with BT474 cells. Inferred protein networks were confirmed by observing an up-regulation of IGF-1R and profilin in BT474 and up-regulation of Ras and enolase in SKBR3 using western blot.

Conclusion

When interpreted in the context of prior information, our results suggest that the overall patterns of differential protein expression obtained from limited samples can still aid in clinical decision making by providing an estimate of the predominant pathways that underpin cellular phenotype.

Inferring relevant control mechanisms for interleukin-12 signaling in naïve CD4+ T cells

Interleukin-12 (IL-12) is a key cytokine involved in shaping the cell-mediated immunity to intracellular pathogens. IL-12 initiates a cellular response through the IL-12 signaling pathway, a member of the Janus kinase/signal transducer and activator of transcription (JAK/STAT) family of signaling networks. The JAK/STAT pathway includes several regulatory elements; however, the dynamics of these mechanisms are not fully understood. Therefore, the objective of this study was to infer the relative importance of regulatory mechanisms that modulate the activation of STAT4 in naïve CD4(+) T cells. Dynamic changes in protein expression and activity were measured using flow cytometry and these data were used to calibrate a mathematical model of IL-12 signaling. An empirical Bayesian approach was used to infer the relative strengths of the different regulatory mechanisms in the system. The model predicted that IL-12 receptor expression is regulated by a dynamic, autonomous program that was independent of STAT4 activation. In summary, a mathematical model of the canonical IL-12 signaling pathway used in conjunction with a Bayesian framework provided high-confidence predictions of the system-specific control mechanisms from the available experimental observations.

Signal transduction networks in cancer: quantitative parameters influence network topology

Networks of fixed topology are used to summarize the collective understanding of the flow of signaling information within a cell (i.e., canonical signaling networks). Moreover, these canonical signaling networks are used to interpret how observed oncogenic changes in protein activity or expression alter information flow in cancer cells. However, creating a novel branch within a signaling network (i.e., a noncanonical edge) provides a mechanism for a cell to acquire the hallmark characteristics of cancer. The objective of this study was to assess the existence of a noncanonical edge within a receptor tyrosine kinase (RTK) signaling network based upon variation in protein expression alone, using a mathematical model of the early signaling events associated with epidermal growth factor receptor 1 (ErbB1) signaling network as an illustrative example. The abundance of canonical protein-RTK complexes (e.g., growth factor receptor bound protein 2-ErbB1 and Src homology 2 domain containing transforming protein 1-ErbB1) were used to establish a threshold that was correlated with ligand-dependent changes in cell proliferation. Given the available data, the uncertainty associated with this threshold was estimated using an empirical Bayesian approach. Using the variability in protein expression observed among a collection of breast cancer cell lines, this model was used to assess whether a noncanonical edge (e.g., Irs1-ErbB1) exceeds the threshold and to identify cell lines where this noncanonical edge is likely to be observed. Taken together, the simulations suggest that the topology of signal transduction networks within cells is influenced by quantitative parameters, such as protein expression and binding affinity. Moreover, forming this noncanonical pathway was not due solely to overexpression of the cell surface receptor but was influenced by overexpression of all members of the multiprotein complex. Multivariate alterations in expression of signaling proteins in cancer cells may activate noncanonical pathways and may rewire the signaling network within a cell.