Signal transduction at point-blank range: analysis of a spatial coupling mechanism for pathway crosstalk

Rebinding in biochemical reactions on membranes

The behavior of many biochemical processes depends crucially on molecules rapidly rebinding after dissociating. In the case of multisite protein modification, the importance of rebinding has been demonstrated both experimentally and through several recent computational studies involving stochastic spatial simulations. As rebinding stems from spatio-temporal correlations, theorists have resorted to models that explicitly include space to properly account for the effects of rebinding. However, for reactions in three space dimensions it was recently shown that well-mixed ordinary differential equation (ODE) models can incorporate rebinding by adding connections to the reaction network. The rate constants for these new connections involve the probability that a pair of molecules rapidly rebinds after dissociation. In order to study biochemical reactions on membranes, in this paper we derive an explicit formula for this rebinding probability for reactions in two space dimensions. We show that ODE models can use the formula to replicate detailed stochastic spatial simulations, and that the formula can predict ultrasensitivity for reactions involving multisite modification of membrane-bound proteins. Further, we compute a new concentration-dependent rebinding probability for reactions in three space dimensions. Our analysis predicts that rebinding plays a much larger role in reactions on membranes compared to reactions in cytoplasm.

The membrane environment can promote or suppress bistability in cell signaling networks

Many key biochemical reactions that mediate signal transduction in cells occur at the cell membrane, yet how the two-dimensional membrane environment influences the collective behavior of signaling networks is poorly understood. We study models of two topologically different signaling pathways that exhibit bistability, examining the effects of reduced protein mobility and increased concentration at the membrane, as well as effects due to differences in spatiotemporal correlations between the membrane environment and three-dimensional cytoplasm. The two model networks represent the distributive enzymatic modification of a protein at multiple sites and the positive feedback-mediated activation of a protein. In both cases, we find that confining proteins to a membrane-like environment can markedly alter the emergent dynamics. For the distributive protein modification network, increased concentration promotes bistability through enhanced protein-protein binding, while lower mobility and membrane-enhanced spatiotemporal correlations suppress bistability. For the positive feedback-mediated activation network, confinement to a membrane environment enhances protein activation, which can induce bistability or stabilize a monostable, active state. Importantly, the influence of the membrane environment on signaling dynamics can be qualitatively different for signaling modules with different network topologies.

Data-driven modelling of receptor tyrosine kinase signalling networks quantifies receptor-specific potencies of PI3K- and Ras-dependent ERK activation

Signal transduction networks in mammalian cells, comprising a limited set of interacting biochemical pathways, are accessed by various growth factor and cytokine receptors to elicit distinct cell responses. This raises the question as to how specificity of the stimulus-response relationship is encoded at the molecular level. It has been proposed that specificity arises not only from the activation of unique signalling pathways, but also from quantitative differences in the activation and regulation of shared receptor-proximal signalling proteins. To address such hypotheses, data sets with greater precision and coverage of experimental conditions will need to be acquired, and rigorous frameworks that codify and parameterize the inherently non-linear relationships among signalling activities will need to be developed. In the present study we apply a systematic approach combining quantitative measurements and mathematical modelling to compare the signalling networks accessed by FGF (fibroblast growth factor) and PDGF (platelet-derived growth factor) receptors in mouse fibroblasts, in which the ERK (extracellular-signal-regulated kinase) cascade is activated by Ras- and PI3K (phosphoinositide 3-kinase)-dependent pathways. We show that, whereas the FGF stimulation of PI3K signalling is relatively weak, this deficiency is compensated for by a more potent Ras-dependent activation of ERK. Thus, as the modelling would predict, the ERK pathway is activated to a greater extent in cells co-stimulated with FGF and PDGF, relative to the saturated levels achieved with either ligand alone. It is envisaged that similar approaches will prove valuable in the elucidation of quantitative differences among other closely related receptor signalling networks.

A density-dependent switch drives stochastic clustering and polarization of signaling molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered "off" state is desired? And, what limits the spread of clusters when an "on" state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the "neutral drift polarity model." Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.

Quantitative statistical description of integrin clusters in adherent cells

Regulation of protein-protein interactions because of their spatial organisation in cells often shapes cell signalling responses to external stimuli, yet most current cell signalling models do not include spatial segregation of proteins beyond coarse control volumes like the cytosol or nucleus. A significant hindrance to spatial modelling of cell signalling is a lack of data describing the spatial organisation of proteins in cells. One signalling system in which spatial organisation is critical is integrin signalling, where protein interactions are restricted to small, micron-sized protein complexes that form on clusters of transmembrane integrin proteins. Using confocal microscopy and image analysis to quantify the size, shape and location of integrin clusters, the authors observed that cells exhibit large variability in these integrin cluster properties. To describe these heterogeneous populations of clusters quantitatively, the authors identified appropriate probability models to characterise the size, shape and location of integrin clusters in a population of adherent cells. The authors determined that integrin cluster sizes are lognormally distributed, integrin cluster eccentricities are beta distributed, and the distances of integrin clusters from the cell centre are gamma distributed. The authors estimated the parameters corresponding to these probability models from empirical data describing integrin clusters in a population of cells, and the resulting probability models describe the heterogeneous populations of clusters. These population models provide the means to create an accurate mathematical description of spatially localised integrin signalling compartments for use in computational models of integrin signalling.

3-Monoiodothyronamine: the rationale for its action as an endogenous adrenergic-blocking neuromodulator

The investigations reported here were designed to gain insights into the role of 3-monoiodothyronamine (T1AM) in the brain, where the amine was originally identified and characterized. Extensive deiodinase studies indicated that T1AM was derived from the T4 metabolite, reverse triiodothyronine (revT3), while functional studies provided well-confirmed evidence that T1AM has strong adrenergic-blocking effects. Because a state of adrenergic overactivity prevails when triiodothyronine (T3) concentrations become excessive, the possibility that T3's metabolic partner, revT3, might give rise to an antagonist of those T3 actions was thought to be reasonable. All T1AM studies thus far have required use of pharmacological doses. Therefore we considered that choosing a physiological site of action was a priority and focused on the locus coeruleus (LC), the major noradrenergic control center in the brain. Site-directed injections of T1AM into the LC elicited a significant, dose-dependent neuronal firing rate change in a subset of adrenergic neurons with an EC(50)=2.7 microM, a dose well within the physiological range. Further evidence for its physiological actions came from autoradiographic images obtained following intravenous carrier-free (125)I-labeled T1AM injection. These showed that the amine bound with high affinity to the LC and to other selected brain nuclei, each of which is both an LC target and a known T3 binding site. This new evidence points to a physiological role for T1AM as an endogenous adrenergic-blocking neuromodulator in the central noradrenergic system.

Analysis of reaction-diffusion systems with anomalous subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.