Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell surface receptor aggregates Page: 4 of 46
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Steric effects on aggregation
Attempts to simulate cell signaling systems must address the problem of combinatorial complexity
(1), the large numbers of chemical species and reactions that arise from molecular interactions in
these systems. This complexity strains conventional model-specification and simulation approaches,
which take a reaction network (i.e., a list of reactions) as input. An alternative approach to model
specification is to use rules to represent interactions and their consequences (2). In this approach rules
represent generalized reactions, or reaction classes, which arise from molecular interactions !<and
the rules serve as generators of chemical species and reactions. A rule defines a transformation and
the molecular properties and context necessary for a molecule or molecular complex to undergo the
transformation. When the contextual requirements are limited, as when the local environment of a
site determines its reactivity, a set of rules can provide a compact high-level specification of a model
for a system characterized by a large underlying chemical reaction network.
Several software tools have been developed to enable rule-based modeling, including STOCHSIM
"\ BioNetGen (5, 6), Moleculizer (7), Simmune (8), and DYNSTOC (9). Three approaches have
emerged for the simulation of rule-based models. In the "generate-first" approach, rules are iteratively
applied before a simulation to generate a complete list of the possible species and reactions, followed
CJ Vby simulation of the network using either ODEs or Gillespie's Stochastic Simulation Algorithm (SSA)
(2). This approach, which is efficient for small-to-medium sized networks (104 species or less), becomes
computationally intractable as network size grows. Simulation via this approach can be made more
tractable by introducing exact or approximate reductions of a model implied by a given set of rules (10).
The second approach is the "on-the-fly" method which both speeds simulation and limits network
generation from rules, which is expensive(6, 7): On-the-fly simulation takes advantage of a feature -
of methods for simulating discrete-event reaction kinetics, such as the SSA -1-1,J2)that allows lazy .
processing of reaction rules. Namely, to advance a simulation using such a method, we require only
knowledge of the species currently populated and their potential reactions, not all potential species f-C
and reactions. However, in some cases, even the partial reaction network required for on-the-fly
simulation can be exceedingly large (2, 13). The third simulation approach avoids network generation
altogether, and we will refer to it as the "network-free" approach. A variation of this approach,
which is implemented in the SToCHSIM software tool (, was introduced by Morton-Firth and Bray .J&
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Monine, Michael; Posner, Richard; Savage, Paul; Faeder, James & Hlavacek, William S. Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell surface receptor aggregates, article, January 1, 2008; [New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc929629/m1/4/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.