Decoding information in cell shape.

Shape is an indicator of cell health. But how is the information in shape decoded? We hypothesize that decoding occurs by modulation of signaling through changes in plasma membrane curvature. Using analytical approaches and numerical simulations, we studied how elongation of cell shape affects plasma membrane signaling. Mathematical analyses reveal transient accumulation of activated receptors at regions of higher curvature with increasing cell eccentricity. This distribution of activated receptors is periodic, following the Mathieu function, and it arises from local imbalance between reaction and diffusion of soluble ligands and receptors in the plane of the membrane. Numerical simulations show that transient microdomains of activated receptors amplify signals to downstream protein kinases. For growth factor receptor pathways, increasing cell eccentricity elevates the levels of activated cytoplasmic Src and nuclear MAPK1,2. These predictions were experimentally validated by changing cellular eccentricity, showing that shape is a locus of retrievable information storage in cells.

Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks.

The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

ERK regulation of phosphodiesterase 4 enhances dopamine-stimulated AMPA receptor membrane insertion.

AMPA-type glutamate receptor (AMPAR) trafficking is essential for modulating synaptic transmission strength. Prior studies that have characterized signaling pathways underlying AMPAR trafficking have identified the cAMP/PKA-mediated phosphorylation of GluA1, an AMPAR subunit, as a key step in the membrane insertion of AMPAR. Inhibition of ERK impairs AMPAR membrane insertion, but the mechanism by which ERK exerts its effect is unknown. Dopamine, an activator of both PKA and ERK, induces AMPAR insertion, but the relationship between the two protein kinases in the process is not understood. We used a combination of computational modeling and live cell imaging to determine the relationship between ERK and PKA in AMPAR insertion. We developed a dynamical model to study the effects of phosphodiesterase 4 (PDE4), a cAMP phosphodiesterase that is phosphorylated and inhibited by ERK, on the membrane insertion of AMPAR. The model predicted that PKA could be a downstream effector of ERK in regulating AMPAR insertion. We experimentally tested the model predictions and found that dopamine-induced ERK phosphorylates and inhibits PDE4. This regulation results in increased cAMP levels and PKA-mediated phosphorylation of DARPP-32 and GluA1, leading to increased GluA1 trafficking to the membrane. These findings provide unique insight into an unanticipated network topology in which ERK uses PDE4 to regulate PKA output during dopamine signaling. The combination of dynamical models and experiments has helped us unravel the complex interactions between two protein kinase pathways in regulating a fundamental molecular process underlying synaptic plasticity.

G Protein-regulated inducer of neurite outgrowth (GRIN) modulates Sprouty protein repression of mitogen-activated protein kinase (MAPK) activation by growth factor stimulation.

Gα(o/i) interacts directly with GRIN (G protein-regulated inducer of neurite outgrowth). Using the yeast two-hybrid system, we identified Sprouty2 as an interacting partner of GRIN. Gα(o) and Sprouty2 bind to overlapping regions of GRIN, thus competing for GRIN binding. Imaging experiments demonstrated that Gα(o) expression promoted GRIN translocation to the plasma membrane, whereas Sprouty2 expression failed to do so. Given the role of Sprouty2 in the regulation of growth factor-mediated MAPK activation, we examined the contribution of the GRIN-Sprouty2 interaction to CB1 cannabinoid receptor regulation of FGF receptor signaling. In Neuro-2A cells, a system that expresses all of the components endogenously, modulation of GRIN levels led to regulation of MAPK activation. Overexpression of GRIN potentiated FGF activation of MAPK and decreased tyrosine phosphorylation of Sprouty2. Pretreatment with G(o/i)-coupled CB1 receptor agonist attenuated subsequent FGF activation of MAPK. Decreased expression of GRIN both diminished FGF activation of MAPK and blocked CB1R attenuation of MAPK activation. These observations indicate that Gα(o) interacts with GRIN and outcompetes GRIN from bound Sprouty. Free Sprouty then in turn inhibits growth factor signaling. Thus, here we present a novel mechanism of how G(o/i)-coupled receptors can inhibit growth factor signaling to MAPK.

Galphao/i-stimulated proteosomal degradation of RGS20: a mechanism for temporal integration of Gs and Gi pathways.

The G(s) and G(i) pathways interact to control the levels of intracellular cAMP. Although coincident signaling through G(s) and G(i)-coupled receptors can attenuate G(s)-stimulated cAMP levels, it is not known if prior activation of the G(i) pathway can affect signaling by G(s)-coupled receptors. We have found that activated Galpha(o/i) interact with RGS20, a GTPase activating protein for members of the Galpha(omicron/i) family. Interaction between Galpha(o/i) and RGS20 results in decreased cellular levels of RGS20. This decrease was induced by activated Galpha(o) and Galpha(i2) but not by Galpha(q), Galpha(i1) or Galpha(i3.) The Galpha(o/i)-induced decrease in RGS20 can be blocked by proteasomal inhibitors lactacystin or MG132. Activated Galpha(o) stimulates the ubiquitination of RGS20. The serotonin-1A receptor that couples to G(o/i) reduces the levels of RGS20 and this effect is blocked by lactacystin, suggesting that G(o/i) promotes the degradation of RGS20. Expression of RGS20 attenuates the inhibition of beta-adrenergic receptor-induced cAMP levels mediated by the serotonin-1A receptor. Prior activation of the serotonin-1A receptor results in loss of the RGS20-mediated attenuation, and the loss of attenuation is blocked when lactacystin is included during the prior treatment. These observations suggest that G(o/i)-coupled receptors, by stimulating the degradation of RGS20, can regulate how subsequent activation of the G(s) and G(i) pathways controls cellular cAMP levels, thus allowing for signal integration.

An androgen-IL-6-Stat3 autocrine loop re-routes EGF signal in prostate cancer cells.

Dynamic modulation of information flow within signaling networks allows the cell to respond to micro-environmental changes. This property of the cell, while being essential to survival and eliciting appropriate responses, can also be detrimental to the organism by allowing cancerous cells to evade regulation and proliferate. We determined if changes in expression levels of transcriptional regulators and their interactions could alter routing within signaling networks in prostate cancer cells. Increasing the protein levels of the signal transducer and activator of transcription 3 (Stat3) led to Stat3-androgen receptor (AR) complex formation in response to epidermal growth factor (EGF) and interleukin-6 (IL-6) stimulation. Increasing the protein levels of Stat3 increased the EGF induced transcriptional activation of the androgen receptor. Androgen pre-treatment increased Stat3 protein levels in an IL-6 autocrine/paracrine dependent manner in the cells suggesting a feedback loop within cells. Increased Stat3-AR complex leads to a change in the routing of the epidermal growth factor signal allowing the androgen receptor to become activated in a Stat3 dependent manner. Understanding interactions and changes in signal flow within the cell is important to our understanding of signaling networks as well as our ability to identify cellular targets for novel therapies to inhibit cancer progression.

Interconnected network motifs control podocyte morphology and kidney function.

Podocytes are kidney cells with specialized morphology that is required for glomerular filtration. Diseases, such as diabetes, or drug exposure that causes disruption of the podocyte foot process morphology results in kidney pathophysiology. Proteomic analysis of glomeruli isolated from rats with puromycin-induced kidney disease and control rats indicated that protein kinase A (PKA), which is activated by adenosine 3',5'-monophosphate (cAMP), is a key regulator of podocyte morphology and function. In podocytes, cAMP signaling activates cAMP response element-binding protein (CREB) to enhance expression of the gene encoding a differentiation marker, synaptopodin, a protein that associates with actin and promotes its bundling. We constructed and experimentally verified a ß-adrenergic receptor-driven network with multiple feedback and feedforward motifs that controls CREB activity. To determine how the motifs interacted to regulate gene expression, we mapped multicompartment dynamical models, including information about protein subcellular localization, onto the network topology using Petri net formalisms. These computational analyses indicated that the juxtaposition of multiple feedback and feedforward motifs enabled the prolonged CREB activation necessary for synaptopodin expression and actin bundling. Drug-induced modulation of these motifs in diseased rats led to recovery of normal morphology and physiological function in vivo. Thus, analysis of regulatory motifs using network dynamics can provide insights into pathophysiology that enable predictions for drug intervention strategies to treat kidney disease.

Modeling of spatially-restricted intracellular signaling.

Understanding the signaling capabilities of a cell presents a major challenge, not only due to the number of molecules involved, but also because of the complex network connectivity of intracellular signaling. Recently, the proliferation of quantitative imaging techniques has led to the discovery of the vast spatial organization of intracellular signaling. Computational modeling has emerged as a powerful tool for understanding how inhomogeneous signaling originates and is maintained. This article covers the current imaging techniques used to obtain quantitative spatial data and the mathematical approaches used to model spatial cell biology. Modeling-derived hypotheses have been experimentally tested and the integration of modeling and imaging approaches has led to non-intuitive mechanistic insights.

Modeling of spatial intracellular signaling events in neurons.

A neuron is able to seamlessly respond to a number of signals, in a timely and specific manner. This process, of integrating multiple inputs, relays on the orchestration of intracellular events by signaling networks. The inherent complexity of signaling networks has made computational modeling a useful approach to understand their underlying regulatory principles. Recent advances in imaging techniques have highlighted the nonhomogeneous nature of intracellular signaling and its significant contribution to the maintenance of signal specificity. Computational modeling can provide mechanistic insight into the origins of these inhomogeneous distributions of signaling components and their role in the integrative capabilities of the neuron.

Developing models in virtual cell.

This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture on mathematical modeling using the Virtual Cell environment. The lectures discuss the steps involved in developing and running simulations using Virtual Cell, with particular focus on spatial partial differential equation models. We discuss how to construct both ordinary differential equation models, in which the cytoplasm is considered a well-mixed cellular compartment, and partial differential equation models, which calculate how chemical species change as a function of both time and location. The Virtual Cell environment is especially well suited for models that explore spatial specificity of cellular reactions. Partial differential equation models in Virtual Cell can give rise to simulations using predefined cellular geometries, which enable direct comparison with imaging data. These models address questions regarding the regulatory capability arising from spatial organization of the cell. Examples are provided of studies that have successfully exploited the Virtual Cell software to address the spatial contribution to signaling.

Obtaining and estimating kinetic parameters from the literature.

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on strategies for the development of mathematical models. Many biological processes can be represented mathematically as systems of ordinary differential equations (ODEs). Simulations with these mathematical models can provide mechanistic insight into the underlying biology of the system. A prerequisite for running simulations, however, is the identification of kinetic parameters that correspond closely with the biological reality. This lecture presents an overview of the steps required for the development of kinetic ODE models and describes experimental methods that can yield kinetic parameters and concentrations of reactants, which are essential for the development of kinetic models. Strategies are provided to extract necessary parameters from published data. The homework assignment requires students to find parameters appropriate for a well-studied biological regulatory system, convert these parameters into appropriate units, and interpret how different values of these parameters may lead to different biological behaviors.

Models of spatially restricted biochemical reaction systems.

Many reactions within the cell occur only in specific intracellular regions. Such local reaction networks give rise to microdomains of activated signaling components. The dynamics of microdomains can be visualized by live cell imaging. Computational models using partial differential equations provide mechanistic insights into the interacting factors that control microdomain dynamics. The mathematical models show that, for membrane-initiated signaling, the ratio of the surface area of the plasma membrane to the volume of the cytoplasm, the topology of the signaling network, the negative regulators, and kinetic properties of key components together define microdomain dynamics. Thus, patterns of locally restricted signaling reaction systems can be considered an emergent property of the cell.

Specification of spatial relationships in directed graphs of cell signaling networks.

Graph theory provides a useful and powerful tool for the analysis of cellular signaling networks. Intracellular components such as cytoplasmic signaling proteins, transcription factors, and genes are connected by links, representing various types of chemical interactions that result in functional consequences. However, these graphs lack important information regarding the spatial distribution of cellular components. The ability of two cellular components to interact depends not only on their mutual chemical affinity but also on colocalization to the same subcellular region. Localization of components is often used as a regulatory mechanism to achieve specific effects in response to different receptor signals. Here we describe an approach for incorporating spatial distribution into graphs and for the development of mixed graphs where links are specified by mutual chemical affinity as well as colocalization. We suggest that such mixed graphs will provide more accurate descriptions of functional cellular networks and their regulatory capabilities and aid in the development of large-scale predictive models of cellular behavior.

Design logic of a cannabinoid receptor signaling network that triggers neurite outgrowth.

Cannabinoid receptor 1 (CB1R) regulates neuronal differentiation. To understand the logic underlying decision-making in the signaling network controlling CB1R-induced neurite outgrowth, we profiled the activation of several hundred transcription factors after cell stimulation. We assembled an in silico signaling network by connecting CB1R to 23 activated transcription factors. Statistical analyses of this network predicted a role for the breast cancer 1 protein BRCA1 in neuronal differentiation and a new pathway from CB1R through phosphoinositol 3-kinase to the transcription factor paired box 6 (PAX6). Both predictions were experimentally confirmed. Results of transcription factor activation experiments that used pharmacological inhibitors of kinases revealed a network organization of partial OR gates regulating kinases stacked above AND gates that control transcription factors, which together allow for distributed decision-making in CB1R-induced neurite outgrowth.

Role of the Go/i signaling network in the regulation of neurite outgrowth.

Neurite outgrowth is a complex differentiation process stimulated by many neuronal growth factors and transmitters and by electrical activity. Among these stimuli are ligands for G-protein-coupled receptors (GPCR) that function as neurotransmitters. The pathways involved in GPCR-triggered neurite outgrowth are not fully understood. Many of these receptors couple to Galphao, one of the most abundant proteins in the neuronal growth cones. We have studied the Go signaling network involved in neurite outgrowth in Neuro2A cells. Galphao can induce neurite outgrowth. The CB1 cannabinoid receptor, a Go/i-coupled receptor expressed endogenously in Neuro2A cells, triggers neurite outgrowth by activating Rap1, which promotes the Galphao-stimulated proteasomal degradation of Rap1GAPII. CB1-receptor-mediated Rap1 activation leads to the activation of a signaling network that includes the small guanosine triphosphate (GTP)ases Ral and Rac, the protein kinases Src, and c-Jun N-terminal kinase (JNK), which converge onto the activation of signal transducer and activator of transcription 3 (Stat3), a key transcription factor that mediates the gene expression process of neurite outgrowth in Neuro2A cells. This review describes current findings from our laboratory and also discusses alternative pathways that Go/i might mediate to trigger neurite outgrowth. We also analyze the role neurotransmitters, which stimulate Go/i to activate a complex signaling network controlling neurite outgrowth, play in regeneration after neuronal injury.

Modeling of signaling networks.

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.

G protein pathways.

The heterotrimeric guanine nucleotide-binding proteins (G proteins) are signal transducers that communicate signals from many hormones, neurotransmitters, chemokines, and autocrine and paracrine factors. The extracellular signals are received by members of a large superfamily of receptors with seven membrane-spanning regions that activate the G proteins, which route the signals to several distinct intracellular signaling pathways. These pathways interact with one another to form a network that regulates metabolic enzymes, ion channels, transporters, and other components of the cellular machinery controlling a broad range of cellular processes, including transcription, motility, contractility, and secretion. These cellular processes in turn regulate systemic functions such as embryonic development, gonadal development, learning and memory, and organismal homeostasis.