Signal transduction networks allow eukaryotic cells to make decisions based on information about intracellular state and the environment. Biochemical noise significantly diminishes the fidelity of signaling: networks examined to date seem to transmit less than 1 bit of information. It is unclear how networks that control critical cell-fate decisions (e.g., cell division and apoptosis) can function with such low levels of information transfer. Here, we use theory, experiments, and numerical analysis to demonstrate an inherent trade-off between the information transferred in individual cells and the information available to control population-level responses. Noise in receptor-mediated apoptosis reduces information transfer to approximately 1 bit at the single-cell level but allows 3-4 bits of information to be transmitted at the population level. For processes such as eukaryotic chemotaxis, in which single cells are the functional unit, we find high levels of information transmission at a single-cell level. Thus, low levels of information transfer are unlikely to represent a physical limit. Instead, we propose that signaling networks exploit noise at the single-cell level to increase population-level information transfer, allowing extracellular ligands, whose levels are also subject to noise, to incrementally regulate phenotypic changes. This is particularly critical for discrete changes in fate (e.g., life vs. death) for which the key variable is the fraction of cells engaged. Our findings provide a framework for rationalizing the high levels of noise in metazoan signaling networks and have implications for the development of drugs that target these networks in the treatment of cancer and other diseases.

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.

SummaryIn systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

G protein–coupled receptors (GPCRs) are the largest class of cell surface signaling proteins, participate in nearly all physiological processes, and are the targets of 30% of marketed drugs. Typically, nanomolar to micromolar concentrations of ligand are used to activate GPCRs in experimental systems. We detected GPCR responses to a wide range of ligand concentrations, from attomolar to millimolar, by measuring GPCR-stimulated production of cyclic adenosine monophosphate (cAMP) with high spatial and temporal resolution. Mathematical modeling showed that femtomolar concentrations of ligand activated, on average, 40% of the cells in a population provided that a cell was activated by one to two binding events. Furthermore, activation of the endogenous β2-adrenergic receptor (β2AR) and muscarinic acetylcholine M3 receptor (M3R) by femtomolar concentrations of ligand in cell lines and human cardiac fibroblasts caused sustained increases in nuclear translocation of extracellular signal–regulated kinase (ERK) and cytosolic protein kinase C (PKC) activity, respectively. These responses were spatially and temporally distinct from those that occurred in response to higher concentrations of ligand and resulted in a distinct cellular proteomic profile. This highly sensitive signaling depended on the GPCRs forming preassembled, higher-order signaling complexes at the plasma membrane. Recognizing that GPCRs respond to ultralow concentrations of neurotransmitters and hormones challenges established paradigms of drug action and provides a previously unappreciated aspect of GPCR activation that is quite distinct from that typically observed with higher ligand concentrations.

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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.

Rule-based modeling languages, such as the Kappa and BioNetGen languages (BNGL), are powerful frameworks for modeling the dynamics of complex biochemical reaction networks. Each language is distributed with a distinct software suite and modelers may wish to take advantage of both toolsets. This paper introduces a practical application called TRuML that translates models written in either Kappa or BNGL into the other language. While similar in many respects, key di erences between the two languages makes translation su ciently complex that automation becomes a useful tool. TRuML accommodates the languages' complexities and produces a semantically equivalent model in the alternate language of the input model when possible and an approximate model in certain other cases. Here, we discuss a number of these complexities and provide examples of equivalent models in both Kappa and BNGL.

All living things have evolved to sense changes in their environment in order to respond in adaptive ways. At the cellular level, these sensing systems generally involve receptor molecules at the cell surface, which detect changes outside the cell and relay those changes to the appropriate response elements downstream. With the advent of experimental technologies that can track signalling at the single-cell level, it has become clear that many signalling systems exhibit significant levels of ‘noise,’ manifesting as differential responses of otherwise identical cells to the same environment. This noise has a large impact on the capacity of cell signalling networks to transmit information from the environment. Application of information theory to experimental data has found that all systems studied to date encode less than 2.5 bits of information, with the majority transmitting significantly less than 1 bit. Given the growing interest in applying information theory to biological data, it is crucial to understand whether the low values observed to date represent some sort of intrinsic limit on information flow given the inherently stochastic nature of biochemical signalling events. In this work, we used a series of computational models to explore how much information a variety of common ‘signalling motifs’ can encode. We found that the majority of these motifs, which serve as the basic building blocks of cell signalling networks, can encode far more information (4–6 bits) than has ever been observed experimentally. In addition to providing a consistent framework for estimating information-theoretic quantities from experimental data, our findings suggest that the low levels of information flow observed so far in living system are not necessarily due to intrinsic limitations. Further experimental work will be needed to understand whether certain cell signalling systems actually can approach the intrinsic limits described here, and to understand the sources and purpose of the variation that reduces information flow in living cells.