Modeling cell signaling networks

Cell signaling pathways interact with one another to form networks in mammalian systems. Such networks are complex in their organization and exhibit emergent properties such as bistability and ultrasensitivity. Analysis of signaling networks requires a combination of experimental and theoretical approaches including the development and analysis of models. This review focuses on theoretical approaches to understanding cell signaling networks. Using heterotrimeric G protein pathways an example, we demonstrate how interactions between two pathways can result in a network that contains a positive feedback loop and function as a switch. Different mathematical approaches that are currently used to model signaling networks are described, and future challenges including the need for databases as well as enhanced computing environments are discussed.     

Biochemical signaling networks decode temporal patterns of synaptic input

Synapses exhibit a wide repertoire of responses to different temporal patterns of synaptic input. Many of these responses are expressed as short and long-term changes in synaptic strength. Electrical properties of channels and calcium buildup can account for rapid aspects of pattern decoding, but it is not clear how more complex input patterns, especially those lasting over many minutes, could be discriminated. This paper shows that a network of signaling pathways can discriminate between complex input patterns lasting tens of minutes, and can give rise to distinct combinatorial patterns of biochemical signaling activity in pathways involved in synaptic change. Regulatory signaling input can alter and even reverse the strengths of responses to input patterns. Thus the synaptic signaling network may function as a temporal decoder that transforms patterns from the time domain into the domain of chemical signaling. This may underlie different synaptic responses to different stimulus patterns.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1019644427655     

Homeostatic synaptic plasticity: local and global mechanisms for stabilizing neuronal function

Neural circuits must maintain stable function in the face of many plastic challenges, including changes in synapse number and strength, during learning and development. Recent work has shown that these destabilizing influences are counterbalanced by homeostatic plasticity mechanisms that act to stabilize neuronal and circuit activity. One such mechanism is synaptic scaling, which allows neurons to detect changes in their own firing rates through a set of calcium-dependent sensors that then regulate receptor trafficking to increase or decrease the accumulation of glutamate receptors at synaptic sites. Additional homeostatic mechanisms may allow local changes in synaptic activation to generate local synaptic adaptations, and network-wide changes in activity to generate network-wide adjustments in the balance between excitation and inhibition. The signaling pathways underlying these various forms of homeostatic plasticity are currently under intense scrutiny, and although dozens of molecular pathways have now been implicated in homeostatic plasticity, a clear picture of how homeostatic feedback is structured at the molecular level has not yet emerged. On a functional level, neuronal networks likely use this complex set of regulatory mechanisms to achieve homeostasis over a wide range of temporal and spatial scales.     

Roles of the amyloid precursor protein family in the peripheral nervous system

Compelling evidence from in vivo model systems within the past decade shows that the APP family of proteins is important for synaptic development and function in the central and peripheral nervous systems. The synaptic role promises to be complex and multifaceted for several reasons. The three family members have overlapping and redundant functions in mammals. They have both adhesive and signaling properties and may, in principle, act as both ligands and receptors. Moreover, they bind a multitude of synapse-specific proteins, and we predict that additional interacting protein partners will be discovered. Transgenic mice with modified or abolished expression of APP and APLPs have synaptic defects that are readily apparent. Studies of the neuromuscular junction (NMJ) in these transgenic mice have revealed molecular and functional deficits in neurotransmitter release, in organization of the postsynaptic receptors, and in coordinated intercellular development. The results summarized here from invertebrate and vertebrate systems confirm that the NMJ with its accessibility, large size, and homogeneity provides a model synapse for identifying and analyzing molecular pathways of APP actions.     

Dynamic remodeling of scaffold interactions in dendritic spines controls synaptic excitability

Scaffolding proteins interact with membrane receptors to control signaling pathways and cellular functions. However, the dynamics and specific roles of interactions between different components of scaffold complexes are poorly understood because of the dearth of methods available to monitor binding interactions. Using a unique combination of single-cell bioluminescence resonance energy transfer imaging in living neurons and electrophysiological recordings, in this paper, we depict the role of glutamate receptor scaffold complex remodeling in space and time to control synaptic transmission. Despite a broad colocalization of the proteins in neurons, we show that spine-confined assembly/disassembly of this scaffold complex, physiologically triggered by sustained activation of synaptic NMDA (N-methyl-d-aspartate) receptors, induces physical association between ionotropic (NMDA) and metabotropic (mGlu5a) synaptic glutamate receptors. This physical interaction results in an mGlu5a receptor-mediated inhibition of NMDA currents, providing an activity-dependent negative feedback loop on NMDA receptor activity. Such protein scaffold remodeling represents a form of homeostatic control of synaptic excitability.     

Homeostatic signaling: the positive side of negative feedback

Synaptic homeostasis provides a means for neurons and circuits to maintain stable function in the face of perturbations such as developmental or activity-dependent changes in synapse number or strength. These forms of plasticity are thought to utilize negative feedback signaling to sense some aspect of activity, compare this with an internal set point, and then adjust synaptic properties to keep activity close to this set point. However, the molecular identity of these signaling components has not been firmly established. Recent work suggests that there are likely to be multiple forms of synaptic homeostasis, mediated by distinct signaling pathways and with distinct expression mechanisms. These include presynaptic forms that depend on retrograde signaling to presynaptic Ca(2+) channels, and postsynaptic forms influenced by BDNF, TNFalpha and Arc signaling. Current challenges include matching signaling elements to their functions (i.e. as detectors of activity, as part of the set-point mechanism and/or as effectors of synaptic change), and fitting these molecular candidates into a unified view of the signaling pathways that underlie synaptic homeostasis.     

Dynamic characteristics of transient responses

Transient responses of signaling molecules are seen in a wide variety of cellular processes that are mediated by distinct molecular mechanisms. Although transient responses might intuitively be thought to depend on the absolute concentration of growth factors or the intensity of stimulation, we here introduce that some transient responses are prompted by temporal rate of increase of stimulation, rather than intensity of stimulation, by three independent mechanisms. These include the Ras system with fast activation and slow inactivation, the ERK-dependent negative feedback loop system, and the receptor degradation system, all of which can be commonly seen in various signaling networks. In addition, we show the distinct transient and steady state characteristics of these systems.     

Protein kinase signaling in synaptic plasticity and memory

The relay of extracellular signals into changes in cellular physiology involves a Byzantine array of intracellular signaling pathways, of which cytoplasmic protein kinases are a crucial component. In the nervous system, a great deal of effort has focused on understanding the conversion of patterns of synaptic activity into long-lasting changes in synaptic efficacy that are thought to underlie memory. The goal is both to understand synaptic plasticity mechanisms, such as long-term potentiation, at a molecular level and to understand the relationship of these synaptic mechanisms to behavioral memory. Although both involve the activation of multiple signaling pathways, recent studies are beginning to define discrete roles and mechanisms for individual kinases in the different temporal phases of both synaptic and behavioral plasticity.     

Wiring and firing neuronal networks: endocannabinoids take center stage

Endocannabinoids (eCBs) function as retrograde messengers at both excitatory and inhibitory synapses, and control various forms of synaptic plasticity in the adult brain. The molecular machinery required for specific eCB functions during synaptic plasticity is well established. However, eCB signaling plays surprisingly fundamental roles in controlling the acquisition of neuronal identity during CNS development. Recent work suggests that selective recruitment of regulatory signaling networks to CB1 cannabinoid receptors dictates neuronal state-change decisions. In addition, the spatial localization and temporal precision of eCB actions emerges as a novel organizer in developing neuronal networks. Current challenges include fitting novel molecular candidates into regulatory eCB signaling pathways, and defining the temporal dynamics of context-dependent signaling mechanisms underpinning particular neuronal specification events.     

In vitro studies of closed-loop feedback and electrosensory processing in Apteronotus leptorhynchus

Electrosensory systems comprise extensive feedback pathways. It is also well known that these pathways exhibit synaptic plasticity on a wide-range of time scales. Recent in vitro brain slice studies have characterized synaptic plasticity in the two main feedback pathways to the electrosensory lateral line lobe (ELL), a primary electrosensory nucleus in Apteronotus leptorhynchus. Currently-used slice preparations, involving networks in open-loop conditions, allow feedback inputs to be studied in isolation, a critical step in determining their synaptic properties. However, to fully understand electrosensory processing, we must understand how dynamic feedback modulates neuronal responses under closed-loop conditions. To bridge the gap between current in vitro approaches and more complex in vivo work, we present two new in vitro approaches for studying the roles of closed-loop feedback in electrosensory processing. The first involves a hybrid-network approach using dynamic clamp, and the second involves a new slice preparation that preserves one of the feedback pathways to ELL in a closed-loop condition.     

Spatiotemporal Spike Coding of Behavioral Adaptation in the Dorsal Anterior Cingulate Cortex

The frontal cortex controls behavioral adaptation in environments governed by complex rules. Many studies have established the relevance of firing rate modulation after informative events signaling whether and how to update the behavioral policy. However, whether the spatiotemporal features of these neuronal activities contribute to encoding imminent behavioral updates remains unclear. We investigated this issue in the dorsal anterior cingulate cortex (dACC) of monkeys while they adapted their behavior based on their memory of feedback from past choices. We analyzed spike trains of both single units and pairs of simultaneously recorded neurons using an algorithm that emulates different biologically plausible decoding circuits. This method permits the assessment of the performance of both spike-count and spike-timing sensitive decoders. In response to the feedback, single neurons emitted stereotypical spike trains whose temporal structure identified informative events with higher accuracy than mere spike count. The optimal decoding time scale was in the range of 70–200 ms, which is significantly shorter than the memory time scale required by the behavioral task. Importantly, the temporal spiking patterns of single units were predictive of the monkeys’ behavioral response time. Furthermore, some features of these spiking patterns often varied between jointly recorded neurons. All together, our results suggest that dACC drives behavioral adaptation through complex spatiotemporal spike coding. They also indicate that downstream networks, which decode dACC feedback signals, are unlikely to act as mere neural integrators.     

Electrical signaling in the olfactory bulb

The olfactory bulb employs lateral and feedback inhibitory pathways to distribute odor information across parallel assemblies of mitral and granule cells. The pathways involve dendritic action potentials that can interact with a variety of voltage-dependent conductances and synaptic transmission to produce complex and dynamic patterns of activity. Electrical coupling also helps to ensure proper coordination and synchronization of these patterns. These mechanisms provide numerous options for dynamic modulation and control of signaling in the olfactory bulb.     

Dynamic clamp analysis of synaptic integration in sympathetic ganglia

Advances in modern neuroscience require the identification of principles that connect different levels of experimental analysis, from molecular mechanisms to explanations of cellular functions, then to circuits, and, ultimately, to systems and behavior. Here, we examine how synaptic organization of the sympathetic ganglia may enable them to function as use-dependent amplifiers of preganglionic activity and how the gain of this amplification may be modulated by metabotropic signaling mechanisms. The approach combines a general computational model of ganglionic integration together with experimental tests of the model using the dynamic clamp method. In these experiments, we recorded intracellularly from dissociated bullfrog sympathetic neurons and then mimicked physiological synapses with virtual computer-generated synapses. It, thus, became possible to analyze the synaptic gain by recording cellular responses to complex patterns of synaptic activity that normally arise in vivo from convergent nicotinic and muscarinic synapses. The results of these studies are significant because they illustrate how gain generated through ganglionic integration may contribute to the feedback control of important autonomic behaviors, in particular to the control of the blood pressure. We dedicate this paper to the memory of Professor Vladimir Skok, whose rich legacy in synaptic physiology helped to establish the modern paradigm for connecting multiple levels of analysis in studies of the nervous system. Neirofiziologiya/Neurophysiology, Vol. 39, No. 6, pp. 486–492, November–December, 2007.     

Pattern Association and Consolidation Emerges from Connectivity Properties between Cortex and Hippocampus

The basic structure of the cortico-hippocampal system is highly conserved across mammalian species. Comparatively few hippocampal neurons can represent and address a multitude of cortical patterns, establish associations between cortical patterns and consolidate these associations in the cortex. In this study, we investigate how elementary anatomical properties in the cortex-hippocampus loop along with synaptic plasticity contribute to these functions. Specifically, we focus on the high degree of connectivity between cortex and hippocampus leading to converging and diverging forward and backward projections and heterogenous synaptic transmission delays that result from the detached location of the hippocampus and its multiple loops. We found that in a model incorporating these concepts, each cortical pattern can evoke a unique spatio-temporal spiking pattern in hippocampal neurons. This hippocampal response facilitates a reliable disambiguation of learned associations and a bridging of a time interval larger than the time window of spike-timing dependent plasticity in the cortex. Moreover, we found that repeated retrieval of a stored association leads to a compression of the interval between cue presentation and retrieval of the associated pattern from the cortex. Neither a high degree of connectivity nor heterogenous synaptic delays alone is sufficient for this behavior. We conclude that basic anatomical properties between cortex and hippocampus implement mechanisms for representing and consolidating temporal information. Since our model reveals the observed functions for a range of parameters, we suggest that these functions are robust to evolutionary changes consistent with the preserved function of the hippocampal loop across different species.     

Mathematical and computational analysis of adaptation via feedback inhibition in signal transduction pathways

We perform a systematic analysis of mechanisms of feedback regulation that underlie short-term adaptation in intracellular signaling systems. Upon receiving an external cue, these systems generate a transient response that quickly returns to basal levels even if the stimulus persists. Signaling pathways capable of short-term adaptation are found in systems as diverse as the high osmolarity response of yeast, gradient sensing in Dictyostelium, and the cytokine response in vertebrates. Using mathematical analysis and computational experiments, we compare different feedback architectures in terms of response amplitude and duration, ability to adapt, and response to variable stimulus levels. Our analysis reveals three important features of these systems: 1), multiple step signaling cascades improve sensitivity to low doses by an effect distinct from signal amplification; 2), some feedback architectures act as signal transducers converting stimulus strength into response duration; and 3), feedback deactivation acts as a dose-dependent switch between transient and sustained responses. Finally, we present characteristic features for each form of feedback regulation that can aid in their identification.     

A presynaptic endosomal trafficking pathway controls synaptic growth signaling

Structural remodeling of synapses in response to growth signals leads to long-lasting alterations in neuronal function in many systems. Synaptic growth factor receptors alter their signaling properties during transit through the endocytic pathway, but the mechanisms controlling cargo traffic between endocytic compartments remain unclear. Nwk (Nervous Wreck) is a presynaptic F-BAR/SH3 protein that regulates synaptic growth signaling in Drosophila melanogaster. In this paper, we show that Nwk acts through a physical interaction with sorting nexin 16 (SNX16). SNX16 promotes synaptic growth signaling by activated bone morphogenic protein receptors, and live imaging in neurons reveals that SNX16-positive early endosomes undergo transient interactions with Nwk-containing recycling endosomes. We identify an alternative signal termination pathway in the absence of Snx16 that is controlled by endosomal sorting complex required for transport (ESCRT)-mediated internalization of receptors into the endosomal lumen. Our results define a presynaptic trafficking pathway mediated by SNX16, NWK, and the ESCRT complex that functions to control synaptic growth signaling at the interface between endosomal compartments.     

Control of βAR- and N-methyl-D-aspartate (NMDA) Receptor-Dependent cAMP Dynamics in Hippocampal Neurons

Norepinephrine, a neuromodulator that activates β-adrenergic receptors (βARs), facilitates learning and memory as well as the induction of synaptic plasticity in the hippocampus. Several forms of long-term potentiation (LTP) at the Schaffer collateral CA1 synapse require stimulation of both βARs and N-methyl-D-aspartate receptors (NMDARs). To understand the mechanisms mediating the interactions between βAR and NMDAR signaling pathways, we combined FRET imaging of cAMP in hippocampal neuron cultures with spatial mechanistic modeling of signaling pathways in the CA1 pyramidal neuron. Previous work implied that cAMP is synergistically produced in the presence of the βAR agonist isoproterenol and intracellular calcium. In contrast, we show that when application of isoproterenol precedes application of NMDA by several minutes, as is typical of βAR-facilitated LTP experiments, the average amplitude of the cAMP response to NMDA is attenuated compared with the response to NMDA alone. Models simulations suggest that, although the negative feedback loop formed by cAMP, cAMP-dependent protein kinase (PKA), and type 4 phosphodiesterase may be involved in attenuating the cAMP response to NMDA, it is insufficient to explain the range of experimental observations. Instead, attenuation of the cAMP response requires mechanisms upstream of adenylyl cyclase. Our model demonstrates that Gs-to-Gi switching due to PKA phosphorylation of βARs as well as Gi inhibition of type 1 adenylyl cyclase may underlie the experimental observations. This suggests that signaling by β-adrenergic receptors depends on temporal pattern of stimulation, and that switching may represent a novel mechanism for recruiting kinases involved in synaptic plasticity and memory.