Molecular machines or pleiomorphic ensembles: signaling complexes revisited

Phase separation and molecular ordering of the prion-like domain of the Arabidopsis thermosensory protein EARLY FLOWERING 3

Liquid-liquid phase separation (LLPS) is an important mechanism enabling the dynamic compartmentalization of macromolecules, including complex polymers such as proteins and nucleic acids, and occurs as a function of the physicochemical environment. In the model plant, Arabidopsis thaliana, LLPS by the protein EARLY FLOWERING3 (ELF3) occurs in a temperature-sensitive manner and controls thermoresponsive growth. ELF3 contains a largely unstructured prion-like domain (PrLD) that acts as a driver of LLPS in vivo and in vitro. The PrLD contains a poly-glutamine (polyQ) tract, whose length varies across natural Arabidopsis accessions. Here, we use a combination of biochemical, biophysical, and structural techniques to investigate the dilute and condensed phases of the ELF3 PrLD with varying polyQ lengths. We demonstrate that the dilute phase of the ELF3 PrLD forms a monodisperse higher-order oligomer that does not depend on the presence of the polyQ sequence. This species undergoes LLPS in a pH- and temperature-sensitive manner and the polyQ region of the protein tunes the initial stages of phase separation. The liquid phase rapidly undergoes aging and forms a hydrogel as shown by fluorescence and atomic force microscopies. Furthermore, we demonstrate that the hydrogel assumes a semiordered structure as determined by small-angle X-ray scattering, electron microscopy, and X-ray diffraction. These experiments demonstrate a rich structural landscape for a PrLD protein and provide a framework to describe the structural and biophysical properties of biomolecular condensates.

MolClustPy: a Python package to characterize multivalent biomolecular clusters

SUMMARY

Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become supply-limited large clusters. In stochastic simulations, such clusters display a wide range of sizes and compositions. We have developed a Python package, MolClustPy, which performs multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator); MolClustPy characterizes and visualizes the distribution of cluster sizes, molecular composition, and bonds across molecular clusters. The statistical analysis offered by MolClustPy is readily applicable to other stochastic simulation software, such as SpringSaLaD and ReaDDy.

AVAILABILITY AND IMPLEMENTATION

The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide, and examples are freely available at https://molclustpy.github.io/.

The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless compartments known as condensates. As opposed to single-component (homotypic) systems, the concentration dependence of multicomponent (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multicomponent systems. In this study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intracluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the SP profiles. The interplay of flexibility, length, and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when SPs are normalized to nondimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering versus concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates.

MolClustPy: A Python Package to Characterize Multivalent Biomolecular Clusters

S ummary

Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become extra-large clusters. Characterizing the physical properties of these clusters is important in recent biophysical research. Due to weak interactions such clusters are highly stochastic, demonstrating a wide range of sizes and compositions. We have developed a Python package to perform multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator), characterize and visualize the distribution of cluster sizes, molecular composition, and bonds across molecular clusters and individual molecules of different types.

A vailability and implementation

The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide and examples are freely available at https://molclustpy.github.io/.

C ontact

achattaraj007@gmail.com , blinov@uchc.edu.

S upplementary information

Available at https://molclustpy.github.io/.

Targeted Quantification of Protein Phosphorylation and Its Contributions towards Mathematical Modeling of Signaling Pathways

Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)-also known as multiple reaction monitoring (MRM)-and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.

Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network

Dynamic modelling has considerably improved our understanding of complex molecular mechanisms. Ordinary differential equations (ODEs) are the most detailed and popular approach to modelling the dynamics of molecular systems. However, their application in signalling networks, characterised by multi-state molecular complexes, can be prohibitive. Contemporary modelling methods, such as rule- based (RB) modelling, have addressed these issues. The advantages of RB modelling over ODEs have been presented and discussed in numerous reviews. In this study, we conduct a direct comparison of the time courses of a molecular system founded on the same reaction network but encoded in the two frameworks. To make such a comparison, a set of reactions that underlie an ODE model was manually encoded in the Kappa language, one of the RB implementations. A comparison of the models was performed at the level of model specification and dynamics, acquired through model simulations. In line with previous reports, we confirm that the Kappa model recapitulates the general dynamics of its ODE counterpart with minor differences. These occur when molecules have multiple sites binding the same interactor. Furthermore, activation of these molecules in the RB model is slower than in the ODE one. As reported for other molecular systems, we find that, also for the DARPP-32 reaction network, the RB representation offers a more expressive and flexible syntax that facilitates access to fine details of the model, easing model reuse. In parallel with these analyses, we report a refactored model of the DARPP-32 interaction network that can serve as a canvas for the development of more complex dynamic models to study this important molecular system.

Artifacts and levels of abstraction

The purpose of this article is to show how the comparison or analogy with artifacts (i.e., systems engineered by humans) is foundational for the idea that complex neuro-cognitive systems are amenable to explanation at distinct levels, which is a central simplifying strategy for modeling the brain. The most salient source of analogy is of course the digital computer, but I will discuss how some more general comparisons with the processes of design and engineering also play a significant role. I will show how the analogies, and the subsequent notion of a distinct computational level, have engendered common ideas about how safely to abstract away from the complexity of concrete neural systems, yielding explanations of how neural processes give rise to cognitive functions. I also raise worries about the limitations of these explanations, due to neglected differences between the human-made devices and biological organs.

The solubility product extends the buffering concept to heterotypic biomolecular condensates

Biomolecular condensates are formed by liquid-liquid phase separation (LLPS) of multivalent molecules. LLPS from a single ("homotypic") constituent is governed by buffering: above a threshold, free monomer concentration is clamped, with all added molecules entering the condensed phase. However, both experiment and theory demonstrate that buffering fails for the concentration dependence of multicomponent ("heterotypic") LLPS. Using network-free stochastic modeling, we demonstrate that LLPS can be described by the solubility product constant (Ksp): the product of free monomer concentrations, accounting for the ideal stoichiometries governed by the valencies, displays a threshold above which additional monomers are funneled into large clusters; this reduces to simple buffering for homotypic systems. The Ksp regulates the composition of the dilute phase for a wide range of valencies and stoichiometries. The role of Ksp is further supported by coarse-grained spatial particle simulations. Thus, the solubility product offers a general formulation for the concentration dependence of LLPS.

A developmental perspective of homology and evolutionary novelty

The development and evolution of multicellular body plans is complex. Many distinct organs and body parts must be reproduced at each generation, and those that are traceable over long time scales are considered homologous. Among the most pressing and least understood phenomena in evolutionary biology is the mode by which new homologs, or "novelties" are introduced to the body plan and whether the developmental changes associated with such evolution deserve special treatment. In this chapter, we address the concepts of homology and evolutionary novelty through the lens of development. We present a series of case studies, within insects and vertebrates, from which we propose a developmental model of multicellular organ identity. With this model in hand, we make predictions regarding the developmental evolution of body plans and highlight the need for more integrative analysis of developing systems.

The Relationship between Effective Molarity and Affinity Governs Rate Enhancements in Tethered Kinase-Substrate Reactions

Scaffold proteins are thought to accelerate protein phosphorylation reactions by tethering kinases and substrates together, but there is little quantitative data on their functional effects. To assess the contribution of tethering to kinase reactivity, we compared intramolecular and intermolecular kinase reactions in a minimal model system. We found that tethering can enhance reaction rates in a flexible tethered kinase system and that the magnitude of the effect is sensitive to the structure of the tether. The largest effective molarity we obtained was ∼0.08 μM, which is much lower than the effects observed in small molecule model systems and other tethered protein reactions. We further demonstrated that the tethered intramolecular reaction only makes a significant contribution to the observed rates when the scaffolded complex assembles at concentrations below the effective molarity. These findings provide a quantitative framework that can be applied to understand endogenous protein scaffolds and engineer synthetic networks.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Dynalogo: an interactive sequence logo with dynamic thresholding of matched quantitative proteomic data

SUMMARY

Current web-based sequence logo analyses for studying domain-peptide interactions are often conducted only on high affinity binders due to conservative data thresholding. We have developed Dynalogo, a combination of threshold varying tool and sequence logo generator written in the R statistical programming language, which allows on-the-fly visualization of binding specificity over a wide range of affinity interactions. Hence researchers can easily explore their dataset without the constraint of an arbitrary threshold. After importing quantitative data files, there are various data filtering and visualizing features available. Using a threshold control, users can easily track the dynamic change of enrichment and depletion of amino acid characters in the sequence logo panel. The built-in export function allows downloading filtered data and graphical outputs for further analyses. Dynalogo is optimized for analysis of modular domain-peptide binding experiments but the platform offers a broader application including quantitative proteomics.

AVAILABILITY AND IMPLEMENTATION

Dynalogo application, user manual and sample data files are available at https://dynalogo.cam.uchc.edu. The source code is available at https://github.com/lafontaine-uchc/dynalogo.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Combinatorial protein-protein interactions on a polymerizing scaffold

Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood as stoichiometric aggregates, but as combinatorial ensembles. We analyze the combinatorial interaction of ligands loaded on polymeric scaffolds, in both a continuum and discrete setting, and compare it with multivalent scaffolds with fixed number of binding sites. The quantity of interest is the abundance of ligand interaction possibilities-the catalytic potential Q-in a configurational mixture. Upon increasing scaffold abundance, scaffolding systems are known to first increase opportunities for ligand interaction and then to shut them down as ligands become isolated on distinct scaffolds. The polymerizing system stands out in that the dependency of Q on protomer concentration switches from being dominated by a first order to a second order term within a range determined by the polymerization affinity. This behavior boosts Q beyond that of any multivalent scaffold system. In addition, the subsequent drop-off is considerably mitigated in that Q decreases with half the power in protomer concentration than for any multivalent scaffold. We explain this behavior in terms of how the concentration profile of the polymer-length distribution adjusts to changes in protomer concentration and affinity. The discrete case turns out to be similar, but the behavior can be exaggerated at small protomer numbers because of a maximal polymer size, analogous to finite-size effects in bond percolation on a lattice.

Heterogeneity in The Mechanical Properties of Integrins Determines Mechanotransduction Dynamics in Bone Osteoblasts

Bone cells are exposed to dynamic mechanical stimulation that is transduced into cellular responses by mechanotransduction mechanisms. The extracellular matrix (ECM) provides a physical link between loading and bone cells, where mechanoreceptors, such as integrins, initiate mechanosensation. Though this relationship is well studied, the dynamic interplay between mechanosensation, mechanotransduction and cellular responses is unclear. A hybrid-multiscale model combining molecular, cellular and tissue interactions was developed to examine links between integrins’ mechanosensation and effects on mechanotransduction, ECM modulation and cell-ECM interaction. The model shows that altering integrin mechanosensitivity threshold (MT) increases mechanotransduction durations from hours to beyond 4 days, where bone formation starts. This is relevant to bone, where it is known that a brief stimulating period provides persistent influences for over 24 hours. Furthermore, the model forecasts that integrin heterogeneity, with respect to MT, would be able to induce sustained increase in pERK baseline > 15% beyond 4 days. This is analogous to the emergence of molecular mechanical memory signalling dynamics. Therefore, the model can provide a greater understanding of mechanical adaptation to differential mechanical responses at different times. Given reduction of bone sensitivity to mechanical stimulation with age, these findings may lead towards useful therapeutic targets for upregulation of bone mass.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

The Interplay of Structural and Cellular Biophysics Controls Clustering of Multivalent Molecules

Dynamic molecular clusters are assembled through weak multivalent interactions and are platforms for cellular functions, especially receptor-mediated signaling. Clustering is also a prerequisite for liquid-liquid phase separation. It is not well understood, however, how molecular structure and cellular organization control clustering. Using coarse-grained kinetic Langevin dynamics, we performed computational experiments on a prototypical ternary system modeled after membrane-bound nephrin, the adaptor Nck1, and the actin nucleation promoting factor NWASP. Steady-state cluster size distributions favored stoichiometries that optimized binding (stoichiometry matching) but still were quite broad. At high concentrations, the system can be driven beyond the saturation boundary such that cluster size is limited only by the number of available molecules. This behavior would be predictive of phase separation. Domains close to binding sites sterically inhibited clustering much less than terminal domains because the latter effectively restrict access to the cluster interior. Increased flexibility of interacting molecules diminished clustering by shielding binding sites within compact conformations. Membrane association of nephrin increased the cluster size distribution in a density-dependent manner. These properties provide insights into how molecular ensembles function to localize and amplify cell signaling.

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

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

Liquid phase condensation in cell physiology and disease

Phase transitions are ubiquitous in nonliving matter, and recent discoveries have shown that they also play a key role within living cells. Intracellular liquid-liquid phase separation is thought to drive the formation of condensed liquid-like droplets of protein, RNA, and other biomolecules, which form in the absence of a delimiting membrane. Recent studies have elucidated many aspects of the molecular interactions underlying the formation of these remarkable and ubiquitous droplets and the way in which such interactions dictate their material properties, composition, and phase behavior. Here, we review these exciting developments and highlight key remaining challenges, particularly the ability of liquid condensates to both facilitate and respond to biological function and how their metastability may underlie devastating protein aggregation diseases.

Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface

Motivation

Smoldyn is a spatial and stochastic biochemical simulator. It treats each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions, all with good accuracy. This article presents several new features.

Results

Smoldyn now supports two types of rule-based modeling. These are a wildcard method, which is very convenient, and the BioNetGen package with extensions for spatial simulation, which is better for complicated models. Smoldyn also includes new algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume. Both are exact in the limit of short time steps and reasonably good with longer steps. In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source code can be accessed through a C/C ++ language library interface.

Availability and Implementation

Smoldyn software, documentation, code, and examples are at http://www.smoldyn.org .

Contact

steven.s.andrews@gmail.com.

Compartmental and Spatial Rule-Based Modeling with Virtual Cell

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator.

Multivalent Molecules as Modulators of RNA Granule Size and Composition

RNA granules are ensembles of specific RNA and protein molecules that mediate localized translation in eukaryotic cells. The mechanisms for formation and selectivity of RNA granules are unknown. Here we present a model for assembly of one type of RNA granule based on experimentally measured binding interactions among three core multivalent molecular components necessary for such assembly: specific RNA molecules that contain a cis-acting sequence called the A2 response element (A2RE), hnRNP A2 proteins that bind specifically (with high affinity) to A2RE sequences or nonspecifically (with lower affinity) to other RNA sequences, and heptavalent protein cytoskeleton-associated protein 5 (CKAP5, an alternative name for TOG protein) that binds both hnRNP A2 molecules and RNA. Non-A2RE RNA molecules (RNA without the A2RE sequence) that may be recruited to the granules through nonspecific interactions are also considered in the model. Modeling multivalent molecular interactions in granules is challenging because of combinatorial complexity in the number of potential molecular complexes among these core components and dynamic changes in granule composition and structure in response to changes in local intracellular environment. We use a hybrid modeling approach (deterministic-stochastic-statistical) that is appropriate when the overall compositions of multimolecular ensembles are of greater importance than the specific interactions among individual molecular components. Modeling studies titrating the concentrations of various granule components and varying effective site pair affinities and RNA valency demonstrate that interactions between multivalent components (TOG and RNA) are modulated by a bivalent adaptor molecule (hnRNP A2). Formation and disruption of granules, as well as RNA selectivity in granule composition are regulated by distinct concentration regimes of A2. Our results suggest that granule assembly is tightly controlled by multivalent molecular interactions among RNA molecules, adaptor proteins, and scaffold proteins.

The oxidative stress theory of disease: levels of evidence and epistemological aspects

The theory that oxidative stress (OS) is at the root of several diseases is extremely popular. However, so far, no antioxidant has been recommended or offered by healthcare systems neither has any been approved as therapy by regulatory agencies that base their decisions on evidence-based medicine. This is simply because, so far, despite many preclinical and clinical studies indicating a beneficial effect of antioxidants in many disease conditions, randomised clinical trials have failed to provide the evidence of efficacy required for drug approval. In this review, we discuss the levels of evidence required to claim causality in preclinical research on OS, the weakness of the oversimplification associated with OS theory of disease and the importance of the narrative in its popularity. Finally, from a more translational perspective, we discuss the reasons why antioxidants acting by scavenging ROS might not only prevent their detrimental effects but also interfere with essential signalling roles. We propose that ROS have a complex metabolism and are generated by different enzymes at diverse sites and at different times. Aggregating this plurality of systems into a single theory of disease may not be the best way to develop new drugs, and future research may need to focus on specific oxygen-toxifying pathways rather than on non-specific ROS scavengers. Finally, similarly to what is nowadays required for clinical trials, we recommend making unpublished data available in repositories (open data), as this will allow big data approaches or meta-analyses, without the drawbacks of publication bias.

LINKED ARTICLES

This article is part of a themed section on Redox Biology and Oxidative Stress in Health and Disease. To view the other articles in this section visit http://onlinelibrary.wiley.com/doi/10.1111/bph.v174.12/issuetoc.

Rule-based modeling with Virtual Cell

Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine.

AVAILABILITY AND IMPLEMENTATION

Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user's computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge.

CONTACT

vcell_support@uchc.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

SpringSaLaD: A Spatial, Particle-Based Biochemical Simulation Platform with Excluded Volume

We introduce Springs, Sites, and Langevin Dynamics (SpringSaLaD), a comprehensive software platform for spatial, stochastic, particle-based modeling of biochemical systems. SpringSaLaD models biomolecules in a coarse-grained manner as a group of linked spherical sites with excluded volume. This mesoscopic approach bridges the gap between highly detailed molecular dynamics simulations and the various methods used to study network kinetics and diffusion at the cellular level. SpringSaLaD is a standalone tool that supports model building, simulation, visualization, and data analysis, all through a user-friendly graphical user interface that should make it more accessible than tools built into more comprehensive molecular dynamics infrastructures. Importantly, for bimolecular reactions we derive an exact expression relating the macroscopic on-rate to the various microscopic parameters with the inclusion of excluded volume; this makes SpringSaLaD more accurate than other tools, which rely on approximate relationships between these parameters.

Use of mechanistic models to integrate and analyze multiple proteomic datasets

Proteins in cell signaling networks tend to interact promiscuously through low-affinity interactions. Consequently, evaluating the physiological importance of mapped interactions can be difficult. Attempts to do so have tended to focus on single, measurable physicochemical factors, such as affinity or abundance. For example, interaction importance has been assessed on the basis of the relative affinities of binding partners for a protein of interest, such as a receptor. However, multiple factors can be expected to simultaneously influence the recruitment of proteins to a receptor (and the potential of these proteins to contribute to receptor signaling), including affinity, abundance, and competition, which is a network property. Here, we demonstrate that measurements of protein copy numbers and binding affinities can be integrated within the framework of a mechanistic, computational model that accounts for mass action and competition. We use cell line-specific models to rank the relative importance of protein-protein interactions in the epidermal growth factor receptor (EGFR) signaling network for 11 different cell lines. Each model accounts for experimentally characterized interactions of six autophosphorylation sites in EGFR with proteins containing a Src homology 2 and/or phosphotyrosine-binding domain. We measure importance as the predicted maximal extent of recruitment of a protein to EGFR following ligand-stimulated activation of EGFR signaling. We find that interactions ranked highly by this metric include experimentally detected interactions. Proteins with high importance rank in multiple cell lines include proteins with recognized, well-characterized roles in EGFR signaling, such as GRB2 and SHC1, as well as a protein with a less well-defined role, YES1. Our results reveal potential cell line-specific differences in recruitment.

Phosphatase specificity and pathway insulation in signaling networks

Phosphatases play an important role in cellular signaling networks by regulating the phosphorylation state of proteins. Phosphatases are classically considered to be promiscuous, acting on tens to hundreds of different substrates. We recently demonstrated that a shared phosphatase can couple the responses of two proteins to incoming signals, even if those two substrates are from otherwise isolated areas of the network. This finding raises a potential paradox: if phosphatases are indeed highly promiscuous, how do cells insulate themselves against unwanted crosstalk? Here, we use mathematical models to explore three possible insulation mechanisms. One approach involves evolving phosphatase KM values that are large enough to prevent saturation by the phosphatase's substrates. Although this is an effective method for generating isolation, the phosphatase becomes a highly inefficient enzyme, which prevents the system from achieving switch-like responses and can result in slow response kinetics. We also explore the idea that substrate degradation can serve as an effective phosphatase. Assuming that degradation is unsaturatable, this mechanism could insulate substrates from crosstalk, but it would also preclude ultrasensitive responses and would require very high substrate turnover to achieve rapid dephosphorylation kinetics. Finally, we show that adaptor subunits, such as those found on phosphatases like PP2A, can provide effective insulation against phosphatase crosstalk, but only if their binding to substrates is uncoupled from their binding to the catalytic core. Analysis of the interaction network of PP2A's adaptor domains reveals that although its adaptors may isolate subsets of targets from one another, there is still a strong potential for phosphatase crosstalk within those subsets. Understanding how phosphatase crosstalk and the insulation mechanisms described here impact the function and evolution of signaling networks represents a major challenge for experimental and computational systems biology.

The discovery of modular binding domains: building blocks of cell signalling

Cell signalling - the ability of a cell to process information from the environment and change its behaviour in response - is a central property of life. Signalling depends on proteins that are assembled from a toolkit of modular domains, each of which confers a specific activity or function. The discovery of modular protein- and lipid-binding domains was a crucial turning point in understanding the logic and evolution of signalling mechanisms.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Evolution of synthetic signaling scaffolds by recombination of modular protein domains

Signaling scaffolds are proteins that interact via modular domains with multiple partners, regulating signaling networks in space and time and providing an ideal platform from which to alter signaling functions. However, to better exploit scaffolds for signaling engineering, it is necessary to understand the full extent of their modularity. We used a directed evolution approach to identify, from a large library of randomly shuffled protein interaction domains, variants capable of rescuing the signaling defect of a yeast strain in which Ste5, the scaffold in the mating pathway, had been deleted. After a single round of selection, we identified multiple synthetic scaffold variants with diverse domain architectures, able to mediate mating pathway activation in a pheromone-dependent manner. The facility with which this signaling network accommodates changes in scaffold architecture suggests that the mating signaling complex does not possess a single, precisely defined geometry into which the scaffold has to fit. These relaxed geometric constraints may facilitate the evolution of signaling networks, as well as their engineering for applications in synthetic biology.

Dissecting the calcium-induced differentiation of human primary keratinocytes stem cells by integrative and structural network analyses

The molecular details underlying the time-dependent assembly of protein complexes in cellular networks, such as those that occur during differentiation, are largely unexplored. Focusing on the calcium-induced differentiation of primary human keratinocytes as a model system for a major cellular reorganization process, we look at the expression of genes whose products are involved in manually-annotated protein complexes. Clustering analyses revealed only moderate co-expression of functionally related proteins during differentiation. However, when we looked at protein complexes, we found that the majority (55%) are composed of non-dynamic and dynamic gene products ('di-chromatic'), 19% are non-dynamic, and 26% only dynamic. Considering three-dimensional protein structures to predict steric interactions, we found that proteins encoded by dynamic genes frequently interact with a common non-dynamic protein in a mutually exclusive fashion. This suggests that during differentiation, complex assemblies may also change through variation in the abundance of proteins that compete for binding to common proteins as found in some cases for paralogous proteins. Considering the example of the TNF-α/NFκB signaling complex, we suggest that the same core complex can guide signals into diverse context-specific outputs by addition of time specific expressed subunits, while keeping other cellular functions constant. Thus, our analysis provides evidence that complex assembly with stable core components and competition could contribute to cell differentiation.

The robustness of a signaling complex to domain rearrangements facilitates network evolution

The broad tolerance of domain-rearranging mutations by a yeast signaling network suggests that signaling complexes have loose spatial constraints, making manipulation and perhaps evolution easier.

The rearrangement of protein domains is known to have key roles in the evolution of signaling networks and, consequently, is a major tool used to synthetically rewire networks. However, natural mutational events leading to the creation of proteins with novel domain combinations, such as in frame fusions followed by domain loss, retrotranspositions, or translocations, to name a few, often simultaneously replace pre-existing genes. Thus, while proteins with new domain combinations may establish novel network connections, it is not clear how the concomitant deletions are tolerated. We investigated the mechanisms that enable signaling networks to tolerate domain rearrangement-mediated gene replacements. Using as a model system the yeast mitogen activated protein kinase (MAPK)-mediated mating pathway, we analyzed 92 domain-rearrangement events affecting 11 genes. Our results indicate that, while domain rearrangement events that result in the loss of catalytic activities within the signaling complex are not tolerated, domain rearrangements can drastically alter protein interactions without impairing function. This suggests that signaling complexes can maintain function even when some components are recruited to alternative sites within the complex. Furthermore, we also found that the ability of the complex to tolerate changes in interaction partners does not depend on long disordered linkers that often connect domains. Taken together, our results suggest that some signaling complexes are dynamic ensembles with loose spatial constraints that could be easily re-shaped by evolution and, therefore, are ideal targets for cellular engineering.

Cells use complex protein interaction networks to sense and process external signals. Proteins involved in signaling are often composed of multiple functional units called domains. Because domains are modular, mutations that rearrange domains among proteins have the potential to result in the creation of novel proteins with altered functions. At an evolutionary timescale, domain rearrangements contribute to the functional diversification of signaling networks; at the shorter timescale of the life of an individual, domain rearrangements can impair cellular functions and lead to disease. Here, we investigated how domain-rearranging mutations alter the function of signaling networks, in particular when these mutations disrupt pre-existing proteins. We used as a model system the yeast mating signaling pathway, which shares many properties with more complex pathways active in human cells. Our results demonstrate that signaling networks are often robust to domain rearrangements that disrupt pre-existing genes. In addition, our experiments suggest a possible mechanism to explain this robustness: rather than being a rigid multi-protein machine, the yeast mating signaling complex is a dynamic ensemble with loose spatial constraints. Because of this, the changes in protein interaction partners caused by domain-rearrangement mutations can be accommodated without disrupting network function.

Reconstitution of multivalent PDZ domain binding to the scaffold protein PSD-95 reveals ternary-complex specificity of combinatorial inhibition

Multidomain scaffold proteins serve as hubs in the signal transduction network. By physically colocalizing sequential steps in a transduction pathway, scaffolds catalyze and direct incoming signals. Much is known about binary interactions with individual domains, but it is unknown whether "scaffolding activity" is predictable from pairwise affinities. Here, we characterized multivalent binding to PSD-95, a scaffold protein containing three PDZ domains connected in series by disordered linkers. We used single molecule fluorescence to watch soluble PSD-95 recruit diffusing proteins to a surface-attached receptor cytoplasmic domain. Different ternary complexes showed unique concentration dependence for scaffolding despite similar pairwise affinity. The concentration dependence of scaffolding activity was not predictable based on binary interactions. PSD-95 did not stabilize specific complexes, but rather increased the frequency of transient binding events. Our results suggest that PSD-95 maintains a loosely connected pleomorphic ensemble rather than forming a stereospecific complex containing all components.

Pleomorphic ensembles: formation of large clusters composed of weakly interacting multivalent molecules

Molecular interactions of importance to cell biology are subject to sol-gel transitions: large clusters of weakly interacting multivalent molecules (gel phase) are produced at a critical concentration of monomers. Examples include cell-cell and cell-matrix adhesions, nucleoprotein bodies, and cell signaling platforms. We use the term pleomorphic ensembles (PEs) to describe these clusters, because they have dynamic compositions and sizes and have rapid turnover of their molecular constituents; this plasticity can be highly responsive to cellular signals. The classical polymer physical chemistry theory developed by Flory and Stockmayer provides a brilliant framework for treating multivalent interactions for simple idealized systems. But the complexity and variability of PEs challenges existing modeling approaches. Here we describe and validate a computational algorithm that extends the Flory-Stockmayer formalism to overcome the limitations of analytic theories. We divide the problem by deterministically calculating the fraction of bound sites for each type of binding site, followed by the stochastic assignment of the bonds to a finite number of molecules. The method allows for high valency within many different kinds of interacting molecules and site types, permits simulation of steady-state distributions, as well as assembly kinetics, and can treat cooperative binding within one of the interacting molecules. We then apply our method to the analysis of interactions in the nephrin-Nck-N-Wasp signaling system, demonstrating how multivalent layered scaffolds produce PEs at low monomer concentrations despite weak binding interactions. We show how the experimental data for this system are most consistent with synergistic cooperative interactions between Nck and N-Wasp.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

Data-driven quantification of the robustness and sensitivity of cell signaling networks

Robustness and sensitivity of responses generated by cell signaling networks has been associated with survival and evolvability of organisms. However, existing methods analyzing robustness and sensitivity of signaling networks ignore the experimentally observed cell-to-cell variations of protein abundances and cell functions or contain ad hoc assumptions. We propose and apply a data-driven maximum entropy based method to quantify robustness and sensitivity of Escherichia coli (E. coli) chemotaxis signaling network. Our analysis correctly rank orders different models of E. coli chemotaxis based on their robustness and suggests that parameters regulating cell signaling are evolutionary selected to vary in individual cells according to their abilities to perturb cell functions. Furthermore, predictions from our approach regarding distribution of protein abundances and properties of chemotactic responses in individual cells based on cell population averaged data are in excellent agreement with their experimental counterparts. Our approach is general and can be used to evaluate robustness as well as generate predictions of single cell properties based on population averaged experimental data in a wide range of cell signaling systems.

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.

MOR is not enough: identification of novel mu-opioid receptor interacting proteins using traditional and modified membrane yeast two-hybrid screens

The mu-opioid receptor (MOR) is the G-protein coupled receptor primarily responsible for mediating the analgesic and rewarding properties of opioid agonist drugs such as morphine, fentanyl, and heroin. We have utilized a combination of traditional and modified membrane yeast two-hybrid screening methods to identify a cohort of novel MOR interacting proteins (MORIPs). The interaction between the MOR and a subset of MORIPs was validated in pulldown, co-immunoprecipitation, and co-localization studies using HEK293 cells stably expressing the MOR as well as rodent brain. Additionally, a subset of MORIPs was found capable of interaction with the delta and kappa opioid receptors, suggesting that they may represent general opioid receptor interacting proteins (ORIPS). Expression of several MORIPs was altered in specific mouse brain regions after chronic treatment with morphine, suggesting that these proteins may play a role in response to opioid agonist drugs. Based on the known function of these newly identified MORIPs, the interactions forming the MOR signalplex are hypothesized to be important for MOR signaling and intracellular trafficking. Understanding the molecular complexity of MOR/MORIP interactions provides a conceptual framework for defining the cellular mechanisms of MOR signaling in brain and may be critical for determining the physiological basis of opioid tolerance and addiction.

Leveraging modeling approaches: reaction networks and rules

We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high-resolution and/or high-throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatiotemporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks - the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks.

Phosphotyrosine signaling proteins that drive oncogenesis tend to be highly interconnected

Mutation and overexpression of receptor tyrosine kinases or the proteins they regulate serve as oncogenic drivers in diverse cancers. To better understand receptor tyrosine kinase signaling and its link to oncogenesis, we used protein microarrays to systematically and quantitatively measure interactions between virtually every SH2 or PTB domain encoded in the human genome and all known sites of tyrosine phosphorylation on 40 receptor tyrosine kinases and on most of the SH2 and PTB domain-containing adaptor proteins. We found that adaptor proteins, like RTKs, have many high affinity bindings sites for other adaptor proteins. In addition, proteins that drive cancer, including both receptors and adaptor proteins, tend to be much more highly interconnected via networks of SH2 and PTB domain-mediated interactions than nononcogenic proteins. Our results suggest that network topological properties such as connectivity can be used to prioritize new drug targets in this well-studied family of signaling proteins.

Crosstalk and competition in signaling networks

Signaling networks have evolved to transduce external and internal information into critical cellular decisions such as growth, differentiation, and apoptosis. These networks form highly interconnected systems within cells due to network crosstalk, where an enzyme from one canonical pathway acts on targets from other pathways. It is currently unclear what types of effects these interconnections can have on the response of networks to incoming signals. In this work, we employ mathematical models to characterize the influence that multiple substrates have on one another. These models build off of the atomistic motif of a kinase/phosphatase pair acting on a single substrate. We find that the ultrasensitive, switch-like response these motifs can exhibit becomes transitive: if one substrate saturates the enzymes and responds ultrasensitively, then all substrates will do so regardless of their degree of saturation. We also demonstrate that the phosphatases themselves can induce crosstalk even when the kinases are independent. These findings have strong implications for how we understand and classify crosstalk, as well as for the rational development of kinase inhibitors aimed at pharmaceutically modulating network behavior.

Logic modeling and the ridiculome under the rug

Logic-derived modeling has been used to map biological networks and to study arbitrary functional interactions, and fine-grained kinetic modeling can accurately predict the detailed behavior of well-characterized molecular systems; at present, however, neither approach comes close to unraveling the full complexity of a cell. The current data revolution offers significant promises and challenges to both approaches - and could bring them together as it has spurred the development of new methods and tools that may help to bridge the many gaps between data, models, and mechanistic understanding.

Have you used logic modeling in your research? It would not be surprising if many biologists would answer no to this hypothetical question. And it would not be true. In high school biology we already became familiar with cartoon diagrams that illustrate basic mechanisms of the molecular machinery operating inside cells. These are nothing else but simple logic models. If receptor and ligand are present, then receptor-ligand complexes form; if a receptor-ligand complex exists, then an enzyme gets activated; if the enzyme is active, then a second messenger is being produced; and so on. Such chains of causality are the essence of logic models (Figure 1a). Arbitrary events and mechanisms are abstracted; relationships are simplified and usually involve just two possible conditions and three possible consequences. The presence or absence of one or more molecule, activity, or function, [some icons in the cartoon] will determine whether another one of them will be produced (created, up-regulated, stimulated) [a 'positive' link] or destroyed (degraded, down-regulated, inhibited) [a 'negative' link], or be unaffected [there is no link]. The icons and links often do not follow a standardized format, but when we look at such a cartoon diagram, we believe that we 'understand' how the system works. Because our brain is easily able to process these relationships, these diagrams allow us to answer two fundamental types of questions related to the system: why (are certain things happening)? What if (we make some changes)?

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

BACKGROUND

Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions.

RESULTS

Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map.

CONCLUSIONS

With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.

A computational model for early events in B cell antigen receptor signaling: analysis of the roles of Lyn and Fyn

BCR signaling regulates the activities and fates of B cells. BCR signaling encompasses two feedback loops emanating from Lyn and Fyn, which are Src family protein tyrosine kinases (SFKs). Positive feedback arises from SFK-mediated trans phosphorylation of BCR and receptor-bound Lyn and Fyn, which increases the kinase activities of Lyn and Fyn. Negative feedback arises from SFK-mediated cis phosphorylation of the transmembrane adapter protein PAG1, which recruits the cytosolic protein tyrosine kinase Csk to the plasma membrane, where it acts to decrease the kinase activities of Lyn and Fyn. To study the effects of the positive and negative feedback loops on the dynamical stability of BCR signaling and the relative contributions of Lyn and Fyn to BCR signaling, we consider in this study a rule-based model for early events in BCR signaling that encompasses membrane-proximal interactions of six proteins, as follows: BCR, Lyn, Fyn, Csk, PAG1, and Syk, a cytosolic protein tyrosine kinase that is activated as a result of SFK-mediated phosphorylation of BCR. The model is consistent with known effects of Lyn and Fyn deletions. We find that BCR signaling can generate a single pulse or oscillations of Syk activation depending on the strength of Ag signal and the relative levels of Lyn and Fyn. We also show that bistability can arise in Lyn- or Csk-deficient cells.

Perspective: Dynamics of receptor tyrosine kinase signaling complexes

Textbook descriptions of signal transduction complexes provide a static snapshot view of highly dynamic events. Despite enormous strides in identifying the key components of signaling complexes and the underlying mechanisms of signal transduction, our understanding of the dynamic behavior of these complexes has lagged behind. Using the example of receptor tyrosine kinases, this perspective takes a fresh look at the dynamics of the system and their potential impact on signal processing.

Combinatorial complexity and compositional drift in protein interaction networks

The assembly of molecular machines and transient signaling complexes does not typically occur under circumstances in which the appropriate proteins are isolated from all others present in the cell. Rather, assembly must proceed in the context of large-scale protein-protein interaction (PPI) networks that are characterized both by conflict and combinatorial complexity. Conflict refers to the fact that protein interfaces can often bind many different partners in a mutually exclusive way, while combinatorial complexity refers to the explosion in the number of distinct complexes that can be formed by a network of binding possibilities. Using computational models, we explore the consequences of these characteristics for the global dynamics of a PPI network based on highly curated yeast two-hybrid data. The limited molecular context represented in this data-type translates formally into an assumption of independent binding sites for each protein. The challenge of avoiding the explicit enumeration of the astronomically many possibilities for complex formation is met by a rule-based approach to kinetic modeling. Despite imposing global biophysical constraints, we find that initially identical simulations rapidly diverge in the space of molecular possibilities, eventually sampling disjoint sets of large complexes. We refer to this phenomenon as "compositional drift". Since interaction data in PPI networks lack detailed information about geometric and biological constraints, our study does not represent a quantitative description of cellular dynamics. Rather, our work brings to light a fundamental problem (the control of compositional drift) that must be solved by mechanisms of assembly in the context of large networks. In cases where drift is not (or cannot be) completely controlled by the cell, this phenomenon could constitute a novel source of phenotypic heterogeneity in cell populations.

Is the philosophy of mechanism philosophy enough?

Recognition of the widespread use of the word 'mechanism' in bio-molecular research has resulted in the concept of 'mechanism' becoming a focal point for a highly visible group of philosophers of biology. Rather, however, than grasping and elucidating the situated aims and practices of biologists themselves, the philosophical investigation of the contemporary meaning of mechanism in biology has been commandeered by the needs of 'hard naturalists' to replace the old deductive-nomological model of the 'received view' with a new normative-explanatory gold-standard. It is argued that rather than an orientation toward an increasingly precise characterization of mechanisms as being an ultimate end in biological research, in actual biological practice 'mechanism' means different things in different contexts, pragmatically draws on our embodied know-how in the use of machines and is not, nor should be, an ultimate end of biological research. Further, it is argued, that classic work on low-level mechanisms became taken up qualitatively as parts of the scaffolding for investigating higher level regulatory processes and that in so doing, and in light of new findings such as that of the regulatory significance of 'pleiomorphic ensembles' and 'intrinsically unstructured proteins' the explanatory limits of the mechanism image have already come into view.

Noise in cellular signaling pathways: causes and effects

Noise caused by stochastic fluctuations in genetic circuits (transcription and translation) is now appreciated as a central aspect of cell function and phenotypic behavior. Noise has also been detected in signaling networks, but the origin of this noise and how it shapes cellular outcomes remain poorly understood. Here, we argue that noise in signaling networks results from the intrinsic promiscuity of protein-protein interactions (PPIs), and that this noise has shaped cellular signal transduction. Features promoted by the presence of this molecular signaling noise include multimerization and clustering of signaling components, pleiotropic effects of gross changes in protein concentration, and a probabilistic rather than a linear view of signal propagation.