Prediction in the face of uncertainty: a Monte Carlo-based approach for systems biology of cancer treatment

Cancer is known to be a complex disease and its therapy is difficult. Much information is available on molecules and pathways involved in cancer onset and progression and this data provides a valuable resource for the development of predictive computer models that can help to identify new potential drug targets or to improve therapies. Modeling cancer treatment has to take into account many cellular pathways usually leading to the construction of large mathematical models. The development of such models is complicated by the fact that relevant parameters are either completely unknown, or can at best be measured under highly artificial conditions. Here we propose an approach for constructing predictive models of such complex biological networks in the absence of accurate knowledge on parameter values, and apply this strategy to predict the effects of perturbations induced by anti-cancer drug target inhibitions on an epidermal growth factor (EGF) signaling network. The strategy is based on a Monte Carlo approach, in which the kinetic parameters are repeatedly sampled from specific probability distributions and used for multiple parallel simulations. Simulation results from different forms of the model (e.g., a model that expresses a certain mutation or mutation pattern or the treatment by a certain drug or drug combination) can be compared with the unperturbed control model and used for the prediction of the perturbation effects. This framework opens the way to experiment with complex biological networks in the computer, likely to save costs in drug development and to improve patient therapy.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

Computational modeling of cellular signaling processes embedded into dynamic spatial contexts

Cellular signaling processes depend on spatiotemporal distributions of molecular components. Multicolor, high-resolution microscopy permits detailed assessment of such distributions, providing input for fine-grained computational models that explore mechanisms governing dynamic assembly of multimolecular complexes and their role in shaping cellular behavior. However, it is challenging to incorporate into such models both complex molecular reaction cascades and the spatial localization of signaling components in dynamic cellular morphologies. Here we introduce an approach to address these challenges by automatically generating computational representations of complex reaction networks based on simple bimolecular interaction rules embedded into detailed, adaptive models of cellular morphology. Using examples of receptor-mediated cellular adhesion and signal-induced localized mitogen-activated protein kinase (MAPK) activation in yeast, we illustrate the capacity of this simulation technique to provide insights into cell biological processes. The modeling algorithms, implemented in a new version of the Simmune toolset, are accessible through intuitive graphical interfaces and programming libraries.     

Viruses associated with human cancer

It is estimated that viral infections contribute to 15-20% of all human cancers. As obligatory intracellular parasites, viruses encode proteins that reprogram host cellular signaling pathways that control proliferation, differentiation, cell death, genomic integrity, and recognition by the immune system. These cellular processes are governed by complex and redundant regulatory networks and are surveyed by sentinel mechanisms that ensure that aberrant cells are removed from the proliferative pool. Given that the genome size of a virus is highly restricted to ensure packaging within an infectious structure, viruses must target cellular regulatory nodes with limited redundancy and need to inactivate surveillance mechanisms that would normally recognize and extinguish such abnormal cells. In many cases, key proteins in these same regulatory networks are subject to mutation in non-virally associated diseases and cancers. Oncogenic viruses have thus served as important experimental models to identify and molecularly investigate such cellular networks. These include the discovery of oncogenes and tumor suppressors, identification of regulatory networks that are critical for maintenance of genomic integrity, and processes that govern immune surveillance.     

Domain-mediated protein interaction prediction: From genome to network

Protein-protein interactions (PPIs), involved in many biological processes such as cellular signaling, are ultimately encoded in the genome. Solving the problem of predicting protein interactions from the genome sequence will lead to increased understanding of complex networks, evolution and human disease. We can learn the relationship between genomes and networks by focusing on an easily approachable subset of high-resolution protein interactions that are mediated by peptide recognition modules (PRMs) such as PDZ, WW and SH3 domains. This review focuses on computational prediction and analysis of PRM-mediated networks and discusses sequence- and structure-based interaction predictors, techniques and datasets for identifying physiologically relevant PPIs, and interpreting high-resolution interaction networks in the context of evolution and human disease.     

The statistical mechanics of complex signaling networks: nerve growth factor signaling

The inherent complexity of cellular signaling networks and their importance to a wide range of cellular functions necessitates the development of modeling methods that can be applied toward making predictions and highlighting the appropriate experiments to test our understanding of how these systems are designed and function. We use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. A key difficulty with signaling models is that, while significant effort is being made to experimentally measure the rate constants for individual steps in these networks, many of the parameters required to describe their behavior remain unknown or at best represent estimates. To establish the usefulness of our approach, we have applied our methods toward modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. In particular, we study the actions of NGF and mitogenic epidermal growth factor (EGF) in rat pheochromocytoma (PC12) cells. Through a network of intermediate signaling proteins, each of these growth factors stimulates extracellular regulated kinase (Erk) phosphorylation with distinct dynamical profiles. Using our modeling approach, we are able to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems that we call 'sloppiness.'     

Dynamic analysis of integrated signaling, metabolic, and regulatory networks

Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes (e.g., metabolism) without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)–based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporating kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and regulatory processes at the genome scale, such as the S. cerevisiae system presented here.     

PKC and PLA2: Probing the complexities of the calcium network

Lipid signaling and phosphorylation cascades are fundamental to calcium signaling networks. In this review, we will discuss the recent laboratory findings for the phospholipase A₂ (PLA₂)/protein kinase C (PKC) pathway within cellular calcium networks. The complexity and connectivity of these ubiquitous cellular signals make interpretation of experimental results extremely challenging. We present here computational methods which have been developed to conquer such complex data, and how they can be used to make models capable of accurately predicting cellular responses within multiple calcium signaling pathways. We propose that information obtained from network analysis and computational techniques provides a rich source of knowledge which can be directly translated to the laboratory benchtop.     

Linking structural features of protein complexes and biological function

Protein–protein interaction (PPI) establishes the central basis for complex cellular networks in a biological cell. Association of proteins with other proteins occurs at varying affinities, yet with a high degree of specificity. PPIs lead to diverse functionality such as catalysis, regulation, signaling, immunity, and inhibition, playing a crucial role in functional genomics. The molecular principle of such interactions is often elusive in nature. Therefore, a comprehensive analysis of known protein complexes from the Protein Data Bank (PDB) is essential for the characterization of structural interface features to determine structure–function relationship. Thus, we analyzed a nonredundant dataset of 278 heterodimer protein complexes, categorized into major functional classes, for distinguishing features. Interestingly, our analysis has identified five key features (interface area, interface polar residue abundance, hydrogen bonds, solvation free energy gain from interface formation, and binding energy) that are discriminatory among the functional classes using Kruskal-Wallis rank sum test. Significant correlations between these PPI interface features amongst functional categories are also documented. Salt bridges correlate with interface area in regulator-inhibitors (r = 0.75). These representative features have implications for the prediction of potential function of novel protein complexes. The results provide molecular insights for better understanding of PPIs and their relation to biological functions.     

Boolink: a graphical interface for open access Boolean network simulations and use in guard cell CO2 signaling

Signaling networks are at the heart of almost all biological processes. Most of these networks contain large number of components, and often either the connections between these components are not known or the rate equations that govern the dynamics of soluble signaling components are not quantified. This uncertainty in network topology and parameters can make it challenging to formulate detailed mathematical models. Boolean networks, in which all components are either on or off, have emerged as viable alternatives to detailed mathematical models that contain rate constants and other parameters. Therefore, open-source platforms of Boolean models for community use are desirable. Here, we present Boolink, a freely available graphical user interface that allows users to easily construct and analyze existing Boolean networks. Boolink can be applied to any Boolean network. We demonstrate its application using a previously published network for abscisic acid (ABA)-driven stomatal closure in Arabidopsis spp. (Arabidopsis thaliana). We also show how Boolink can be used to generate testable predictions by extending the network to include CO₂ regulation of stomatal movements. Predictions of the model were experimentally tested, and the model was iteratively modified based on experiments showing that ABA effectively closes Arabidopsis stomata at near-zero CO₂ concentrations (1.5-ppm CO₂). Thus, Boolink enables public generation and the use of existing Boolean models, including the prior developed ABA signaling model with added CO₂ signaling components.

An open-source, graphical interface for the simulation of Boolean networks is presented, applied to an abscisic acid signaling network in guard cells, and extended to include input from CO₂.     

Cellular signaling identifiability analysis: A case study

Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling—the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology.     

Network modeling of signal transduction: establishing the global view

Embryonic development and adult tissue homeostasis are controlled through activation of intracellular signal transduction pathways by extracellular growth factors. In the past, signal transduction has largely been regarded as a linear process. However, more recent data from large-scale and high-throughput experiments indicate that there is extensive cross-talk between individual signaling cascades leading to the notion of a signaling network. The behavior of such complex networks cannot be predicted by simple intuitive approaches but requires sophisticated models and computational simulations. The purpose of such models is to generate experimentally testable hypotheses and to find explanations for unexpected experimental results. Here, we discuss the need for, and the future impact of, mathematical models for exploring signal transduction in different biological contexts such as for example development.     

Quantitative multiplexed profiling of cellular signaling networks using phosphotyrosine-specific DNA-tagged SH2 domains

Deciphering global signaling networks is of great importance for the detailed understanding of cellular signaling processes controlling many important biological functions. Among signaling processes, tyrosine phosphorylation has a central role. At present, adequate techniques for the global characterization of the tyrosine phosphoproteome are lacking, particularly for the analysis of small amounts of protein. By combining the power of PCR amplification with the unique properties of Src homology region 2 (SH2) domains to specifically recognize tyrosine-phosphorylated proteins, we developed a new proteomic approach, termed oligonucleotide-tagged multiplex assay (OTM). For OTM, multiple SH2 domains are labeled by domain-specific oligonucleotide tags, applied as probes to complex protein mixtures in a multiplex reaction and phosphotyrosine-specific interactions are quantified by PCR. Using OTM we reproducibly quantified differential states of tyrosine phosphorylation with high sensitivity and specificity in small amounts of whole cellular extracts as demonstrated for various tumor cell lines and human leukemia samples.     

Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model

Differential equation models that describe the dynamic changes of biochemical signaling states are important tools to understand cellular behavior. An essential task in building such representations is to infer the affinities, rate constants, and other parameters of a model from actual measurement data. However, intuitive measurement protocols often fail to generate data that restrict the range of possible parameter values. Here we utilized a numerical method to iteratively design optimal live-cell fluorescence microscopy experiments in order to reveal pharmacological and kinetic parameters of a phosphatidylinositol 3,4,5-trisphosphate (PIP₃) second messenger signaling process that is deregulated in many tumors. The experimental approach included the activation of endogenous phosphoinositide 3-kinase (PI3K) by chemically induced recruitment of a regulatory peptide, reversible inhibition of PI3K using a kinase inhibitor, and monitoring of the PI3K-mediated production of PIP₃ lipids using the pleckstrin homology (PH) domain of Akt. We found that an intuitively planned and established experimental protocol did not yield data from which relevant parameters could be inferred. Starting from a set of poorly defined model parameters derived from the intuitively planned experiment, we calculated concentration-time profiles for both the inducing and the inhibitory compound that would minimize the predicted uncertainty of parameter estimates. Two cycles of optimization and experimentation were sufficient to narrowly confine the model parameters, with the mean variance of estimates dropping more than sixty-fold. Thus, optimal experimental design proved to be a powerful strategy to minimize the number of experiments needed to infer biological parameters from a cell signaling assay.     

Quantitative phosphoproteomics by mass spectrometry: past, present, and future

Protein phosphorylation-mediated signaling networks regulate much of the cellular response to external stimuli, and dysregulation in these networks has been linked to multiple disease states. Significant advancements have been made over the past decade to enable the analysis and quantification of cellular protein phosphorylation events, but comprehensive analysis of the phosphoproteome is still lacking, as is the ability to monitor signaling at the network level while comprehending the biological implications of each phosphorylation site. In this review we highlight many of the technological advances over the past decade and describe some of the latest applications of these tools to uncover signaling networks in a variety of biological settings. We finish with a concise discussion of the future of the field, including additional advances that are required to link protein phosphorylation analysis with biological insight.     

Modeling of signaling networks

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.