The molecular complexity within a cell may be seen as an evolutionary response to the external complexity of the cell's environment. This suggests that the external environment may be harnessed to interrogate the cell's internal molecular architecture. Cells, however, are not only nonlinear and non-stationary, but also exhibit heterogeneous responses within a clonal, isogenic population. In effect, each cell undertakes its own experiment. Here, we develop a method of cellular interrogation using programmable microfluidic devices which exploits the additional information present in cell-to-cell variation, without requiring model parameters to be fitted to data. We focussed on Ca2+ signalling in response to hormone stimulation, which exhibits oscillatory spiking in many cell types and chose eight models of Ca2+ signalling networks which exhibit similar behaviour in simulation. We developed a nonlinear frequency analysis for non-stationary responses, which could classify models into groups under parameter variation, but found that this question alone was unable to distinguish critical feedback loops. We further developed a nonlinear amplitude analysis and found that the combination of both questions ruled out six of the models as inconsistent with the experimentally-observed dynamics and heterogeneity. The two models that survived the double interrogation were mathematically different but schematically identical and yielded the same unexpected predictions that we confirmed experimentally. Further analysis showed that subtle mathematical details can markedly influence non-stationary responses under parameter variation, emphasising the difficulty of finding a "correct" model. By developing questions for the pathway being studied, and designing more versatile microfluidics, cellular interrogation holds promise as a systematic strategy that can complement direct intervention by genetics or pharmacology.

Cell-surface receptors are the most common target for therapeutic drugs. The design and optimization of next generation synthetic drugs require a detailed understanding of the interaction with their corresponding receptors. Mathematical approximations to study ligand-receptor systems based on reaction kinetics strongly simplify the spatial constraints of the interaction, while full atomistic ligand-receptor models do not allow for a statistical many-particle analysis, due to their high computational requirements. Here we present a generic coarse-grained model for ligand-receptor systems that accounts for the essential spatial characteristics of the interaction, while allowing statistical analysis. The model captures the main features of ligand-receptor kinetics, such as diffusion dependence of affinity and dissociation rates. Our model is used to characterize chimeric compounds, designed to take advantage of the receptor over-expression phenotype of certain diseases to selectively target unhealthy cells. Molecular dynamics simulations of chimeric ligands are used to study how selectivity can be optimized based on receptor abundance, ligand-receptor affinity and length of the linker between both ligand subunits. Overall, this coarse-grained model is a useful approximation in the study of systems with complex ligand-receptor interactions or spatial constraints.

SUMMARY: Molecular networks are often studied in diverse cellular or experimental contexts, with highly context-specific details. Modelling introduces further choices as to levels of mathematical description. The resulting possibilities are difficult to explore rapidly, hampering the integration of modelling and experiment. We have developed Proteus, a web-based, context-specific tool for building compartmentalized, ordinary differential equation (ODE) models. It is inspired by the idea of a molecular 'toolkit' for Ca(2+) signalling. Toolkits in Proteus are context-independent representations of biological systems as sets of components, which may correspond to mechanisms of differing levels of complexity. Users pick and choose components from a toolkit and, for each component, pick and choose from different mechanisms, each of which describes a different instantiation of the component's mechanism. Proteus combines these choices into a system of ODEs, which may then be downloaded in SBML (Systems Biology Markup Language), Matlab or Fortran format and independently analyzed. Toolkits, components and mechanisms are user-constructible, either de novo or by cannibalizing existing models, including all those in the Biomodels database. A wide variety of context-specific models may thereby be rapidly built, modified and explored. AVAILABILITY AND IMPLEMENTATION: Proteus, implemented in C#, and a prototype toolkit for modelling calcium signalling are freely and universally available at www.modularmodeling.com CONTACT: [email protected]; [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.