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WIREs Syst Biol Med
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Rule‐based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

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Rule‐based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model‐specification languages, and recently developed tools designed for specification of rule‐based models allow one to leverage powerful software engineering capabilities. A rule‐based model comprises a set of rules, which can be processed by general‐purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation). WIREs Syst Biol Med 2014, 6:13–36. doi: 10.1002/wsbm.1245 This article is categorized under: Biological Mechanisms > Cell Signaling Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models

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Illustration of how PySB can simplify the specification of related but distinct rules. (a) PySB code that specifies two phosphorylation rules for each of seven sites of insulin‐like growth factor 1 receptor (IGF1R) autophosphorylation. IGF1R is a receptor tyrosine kinase. The rules all have the same form, differing only with respect to substrate and symmetry of ligand binding. It is assumed that an IGF1‐crosslinked receptor can mediate autophosphorylation of sites in both of its monomer subunits. (b) Examples of the 14 rules defined by the PySB code in Panel a, in BioNetGen language (BNGL) format.
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Example of an extended contact map for selected proteins and protein–protein interactions involved in epidermal growth factor receptor (EGFR) signaling. The same proteins and interactions are considered in Figure . Boxes with rounded corners represent selected proteins, domains, and linear motifs. Small square boxes attached to vertical lines represent sites of phosphorylation. Lines that begin and end with an arrowhead represent noncovalent direct‐binding interactions. Lines that begin at a box representing a catalytic subunit and end with a circle point to substrates of an enzyme (a kinase or phosphatase). An open circle indicates a posttranslational modification (phosphorylation); a circle with a line through it indicates reversal of a modification (dephosphorylation). See Table for more information about the interactions represented in this map.
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Example of a contact map for the model of Kiselyov et al. (Figure ). The map shown here is essentially the same as the one that is generated automatically by RuleBender from the model specification that is partially shown in Figure (c).
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A rule‐based model for insulin‐like growth factor 1 (IGF1) interaction with the receptor IGF1R. (a) Two reactions from the model of Kiselyov et al. Reversible capture of a free ligand (IGF1) by an inactive, unbound receptor (IGF1R) is illustrated at left, and reversible ligand‐mediated crosslinking of receptor subunits containing Sites 1 and 2 (or S1 and S2) is illustrated at right. A receptor is dimeric and each monomer contains two ligand‐binding sites. Common shading indicates sites that are found in the same receptor monomer. (b) Two rules from the model of Kiselyov et al. drawn according to the graphical conventions of Faeder et al. The rule at top (bottom) implies the left (right) reaction in Panel a. (c) Excerpts from an executable encoding of the model of Kiselyov et al. in BioNetGen language (BNGL). In the listing shown here, definitions of graphs for IGF1 and IGF1R (i.e., molecule types) are given at top, definitions of seed species are given next, definition of a pattern used in a local function is given in the observables block, and definitions of rules are given at bottom. Rule 1 is the text encoding of the top rule in Panel b, and Rule 3 is the text encoding of the bottom rule in Panel b. Rule 2 is similar to Rule 1. Rules 3 and 4 together define crosslinking of Sites 1 and 2 when a ligand is bound at Site 1. Rule 5 defines crosslinking of Sites 1 and 2 when a ligand is bound at Site 2.
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A protein or protein complex can be represented at different levels of resolution. (a) An atomic model of epidermal growth factor receptor (EGFR) (amino acid residues 25–982). The model is based on experimentally determined structures of three domains of EGFR (PDB accession codes 3NJP, 2M20, and 2JIV). The model does not include the cytoplasmic tail of EGFR. (b) An atomic model of an EGF‐induced oligomer of EGFR, a cyclic side‐by‐side dimer of dimers. EGF is not shown. The model was constructed with preservation of experimentally determined structural interfaces between domains and with preservation of the chemical integrity of individual domains, which were treated as rigid bodies. Consecutive domains are within the allowed lengths of the connecting loops. The top view highlights ectodomain–ectodomain interactions, and the bottom view highlights cytoplasmic domain–cytoplasmic domain interactions. (c) Domain architecture of EGFR. This diagram provides a schematic representation of EGFR and its component parts and includes a depiction of five sites of autophosphorylation (cf. Figures and ). (d) BioNetGen language (BNGL)‐encoded representation of EGF. This encoding indicates that the molecule type EGF contains one functional component, rec. More formally, this line of code introduces a graph that has the color EGF and one vertex labeled rec. (e) BNGL‐encoded representation of EGFR (cf. Panel a). This encoding indicates that the molecule type EGFR has four functional components: lig, back, cd, and Y. The lig component represents the ligand‐binding site, which comprises domains I and III of the EGFR ectodomain. The back component represents domain II of the EGFR ectodomain, which is responsible for a self‐interaction. The cd component, which is responsible for another self‐interaction, represents the cytoplasmic domain of EGFR and encompasses the juxtramembrane region and kinase domain. The cd component is taken to have two possible internal states (or more formally, vertex attributes): closed (c) and open (o). In the o state, the cd component is able to interact with a second copy of itself (also in the o state). The Y component represents an autophosphorylation site, which is taken to have two possible internal states. These states, u and p, represent different phosphorylation states, unphosphorylated, and phosphorylated. (f) BNGL‐encoded representation of a cyclic EGFR tetramer (cf. Panel b). As indicated, this complex is held together through alternating back–back and cd–cd interactions, which are abstractions of the interactions illustrated at atomic resolution in Panel b. Atomic models were visualized using the UCSF Chimera package. The model of Panel b represents only one plausible structure.
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Illustration of proteins and interactions involved in epidermal growth factor receptor (EGFR) signaling. (a) In this graph, nodes correspond to proteins and edges correspond to direct physical interactions. This type of graph is commonly used to visualize protein interaction networks. Numbers next to edges refer to descriptions of interactions given in Table . (b) In this graph, arrows represent positive and negative influences. Note that there is a (negative) arrow connecting PTPN11 and RASA1 even though these proteins do not directly interact (cf. Panels a and b) because PTPN11 is responsible for dephosphorylation of a site in EGFR that interacts with RASA1 (Table ). Interesting regulatory circuits embedded within the diagram of Panel b are highlighted in the panels at bottom. (c) EGFR generates competing positive and negative signals for KRAS activation. (d) An incoherent type 1 feed‐forward loop (FFL) motif. (e) A coherent type 1 FFL motif. (f) A positive feedback loop.
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The edges/arrows of a typical pathway diagram hide significant combinatorial complexity. (a) The interactions and phosphorylation states of the three proteins considered in this diagram [epidermal growth factor receptor (EGFR) and two adaptor proteins, GRB2 and SHC1] imply 11 distinct chemical species. The horizontal bars serve to label the 11 species and to delineate their compositions. Note that EGFR is taken to be phosphorylated at two sites of EGFR autophosphorylation: Y1092 (or both Y1092 and Y1110, which are important docking sites of GRB2) and Y1172 (or both Y1172 and Y1197, which are important docking sites of SHC1). GRB2 and SHC1 interact with EGFR via domains that recognize phosphotyrosines: the SH2 domain in GRB2 and the PTB domain in SHC1. The diagram shown here does not comprehensively depict the known interactions and phosphorylation states of these proteins; for example, EGFR‐mediated phosphorylation of SHC1 and interaction between GRB2 and phosphorylated SHC1 are not considered. (b) The 11 chemical species are connected in a reaction network encompassing 24 unidirectional reactions. Reactions 1–6 are phosphorylation reactions, Reactions 7–12 are dephosphorylation reactions, Reactions 13–18 are bimolecular association reactions, and Reactions 19–24 are dissociation reactions. For simplicity, all reactions are represented as single‐step transformations and catalysts are considered implicitly. For more information about the interactions considered here, see Table .
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Biological Mechanisms > Cell Signaling
Models of Systems Properties and Processes > Mechanistic Models
Analytical and Computational Methods > Computational Methods

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