Internal coarse-graining of molecular systems

Abstract

Modelers of molecular signaling networks must cope with the combinatorial explosion of protein states generated by posttranslational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts wherein specific protein-protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the granularity at which rules specify interactions. We present a formal (and automated) method for constructing a coarsegrained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarsegrained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.protein interaction networks ͉ rule-based models ͉ model reduction ͉ distinguishability ͉ information carriers M olecular biology is spectacularly successful in disassembling cellular systems and anchoring cell-biological behaviors of staggering complexity in chemistry. This raises the challenge of reconstituting molecular systems formally, in pursuit of principles that would make their behavior more intelligible and their control more deliberate. This pursuit is as much driven by the practical need to cure disease as it reflects a desire for a theoretical perspective needed to understand the complexity of cellular phenotypes. In achieving such a perspective, we must deal with two broad problems. First, we must be able to represent and analyze molecular interaction systems of combinatorial complexity. Although ubiquitous, such systems are perhaps most notorious in the context of cellular signaling. The posttranslational modification of proteins and their noncovalent association into transient complexes generate an astronomical number of possible molecular species that can relay signals (1). The question then becomes how to reason about system dynamics if we cannot possibly consider a differential equation for each chemical species that can appear in a system. Second, understanding systems requires resisting the temptation of adopting the view of an outside observer. The outside view is indeed appropriate for the chemical analysis of a network, since the experimenter deliberately interacts in specific ways with the network to create measurable distinctions. Yet, the network, as a dynamical system, may not be capable of making these same distinctions. For example, an experi...

Classic and contemporary approaches to modeling biochemical reactions

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Consolidation and translation regulation: Figure 1.

“…Recently, several rule-based methods have been developed that allow the description of complex molecular systems with essentially no limit to the type or nature of the molecular entities or relationships defined (Bachman and Sorger 2011). The most widely used examples of these are "Kappa Language" (Feret et al 2009) and the "Network-Free Stochastic Simulator" (NFSim) (Sneddon et al 2011), which are capable of integrating static, stochastic, and kinetic representations within the same model. Our understanding of the molecular mechanisms controlling memory consolidation as described in the preceding sections is dominated by two key types of biochemical reaction; binding (protein-protein, miRNA-RNA, and protein-DNA) and site-specific protein phosphorylation.…”

Untangling the protein web

“…A different angle in modelling signalling networks was recently described by Walter Fontana from Harvard University and his colleagues 4 . It uses sets of rules to define relationships between cellular components instead of the more conventional method of defining specific interactions and species using differential equations.…”