Subcellular location of PKA controls striatal plasticity: stochastic simulations in spiny dendrites

IUPHAR review: Computational Psychiatry 2.0. A new tool for supporting combination therapy of psychopharmacology with neuromodulation in schizophrenia

Recent clinical trial successes in schizophrenia with non-dopaminergic agents have rejuvenated the field after a long period of unsuccesfull attempts. At the same time, non-invasive neurostimulation has been increasingly applied in other mental health disorders while a few studies have been performed in schizophrenia. The time has arrived to consider combining psychotherapy with neuromodulation. However, a systematic approach to optimize trial designs is needed. "Computational Psychiatry" has been defined as computational neuroscience modeling using biophysically and anatomically realistic representations of key brain areas based on neuroimaging data and biological knowledge. In this position paper, we will expand this concept to include modeling drug exposure and pharmacology in combination with non-invasive neuromodulation. This computational approach can be used to optimize the impact of psychotherapy and active neuromodulation. This computational platform generates a new in silico biomarker, the "information bandwidth", that might be related to clinical outcomes in schizophrenia. This is based on the assumption that the information processing capacity of the human brain can be represented by a measure of the entropy that quantifies the level of uncertainty associated with the brain processes. Previously we have shown that this readout in a computational neuroscience model of the closed cortical-striatal-thalamocortical loop is highly correlated with clinical changes in positive symptoms after antipsychotic treatment. In this paper we will present a strategy on how this expanded Computational Psychiatry approach can support optimization of clinical trial design combining neuromodulation with psychopharmacology, as well as the understanding and mitigating of the placebo response.

Spatial organization of adenylyl cyclase and its impact on dopamine signaling in neurons

The cAMP cascade is increasingly recognized to transduce physiological effects locally through spatially limited cAMP gradients. However, little is known about how adenylyl cyclase enzymes that initiate cAMP gradients are localized. Here we address this question in physiologically relevant striatal neurons and investigate how AC localization impacts downstream signaling function. We show that the major striatal AC isoforms are differentially sorted between ciliary and extraciliary domains of the plasma membrane, and that one isoform, AC9, is uniquely concentrated in endosomes. We identify key sorting determinants in the N-terminal cytoplasmic domain responsible for isoform-specific localization. We further show that AC9-containing endosomes accumulate activated dopamine receptors and form an elaborately intertwined network with juxtanuclear PKA stores bound to Golgi membranes. Finally, we provide evidence that endosomal localization enables AC9 to selectively elevate PKA activity in the nucleus relative to the cytoplasm. Together, these results reveal a precise spatial landscape of the cAMP cascade in neurons and a key role of AC localization in directing downstream PKA signaling to the nucleus.

Biophysical Modeling of Synaptic Plasticity

Dendritic spines are small, bulbous compartments that function as postsynaptic sites and undergo intense biochemical and biophysical activity. The role of the myriad signaling pathways that are implicated in synaptic plasticity is well studied. A recent abundance of quantitative experimental data has made the events associated with synaptic plasticity amenable to quantitative biophysical modeling. Spines are also fascinating biophysical computational units because spine geometry, signal transduction, and mechanics work in a complex feedback loop to tune synaptic plasticity. In this sense, ideas from modeling cell motility can inspire us to develop multiscale approaches for predictive modeling of synaptic plasticity. In this article, we review the key steps in postsynaptic plasticity with a specific focus on the impact of spine geometry on signaling, cytoskeleton rearrangement, and membrane mechanics. We summarize the main experimental observations and highlight how theory and computation can aid our understanding of these complex processes.

Spatial organization of adenylyl cyclase and its impact on dopamine signaling in neurons

The cAMP cascade is widely recognized to transduce its physiological effects locally through spatially limited cAMP gradients. However, little is known about how the adenylyl cyclase enzymes, which initiate cAMP gradients, are localized. Here we answer this question in physiologically relevant striatal neurons and delineate how AC localization impacts downstream signaling functions. We show that the major striatal AC isoforms are differentially sorted between ciliary and extraciliary domains of the plasma membrane, and that AC9 is uniquely targeted to endosomes. We identify key sorting determinants in the N-terminal cytoplasmic domain responsible for isoform-specific localization. We also show that AC9-containing endosomes accumulate activated dopamine receptors and form an elaborately intertwined network with juxtanuclear PKA stores bound to Golgi membranes. Finally, we show that endosomal localization is critical for AC9 to selectively elevate PKA activity in the nucleus relative to the cytoplasm. These results reveal a precise spatial landscape of the cAMP cascade in neurons and a key role of AC localization in directing downstream signal transduction to the nucleus.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Muscarinic acetylcholine receptor-dependent and NMDA receptor-dependent LTP and LTD share the common AMPAR trafficking pathway

The forebrain cholinergic system promotes higher brain function in part by signaling through the M₁ muscarinic acetylcholine receptor (mAChR). Long-term potentiation (LTP) and long-term depression (LTD) of excitatory synaptic transmission in the hippocampus are also induced by mAChR. An AMPA receptor (AMPAR) trafficking model for hippocampal neurons has been proposed to simulate N-methyl-D-aspartate receptor (NMDAR)-dependent synaptic plasticity in the early phase. In this study, we demonstrated the validity of the hypothesis that the mAChR-dependent LTP/LTD shares a common AMPAR trafficking pathway associated with NMDAR-dependent LTP/LTD. However, unlike NMDAR, Ca²⁺ influx into the spine cytosol occurs owing to the Ca²⁺ stored inside the ER and is induced via the activation of inositol 1,4,5-trisphosphate (IP3) receptors during M1 mAChR activation. Moreover, the AMPAR trafficking model implies that alterations in LTP and LTD observed in Alzheimer's disease could be attributed to age-dependent reductions in AMPAR expression levels.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Integrated regulation of PKA by fast and slow neurotransmission in the nucleus accumbens controls plasticity and stress responses

Cortical glutamate and midbrain dopamine neurotransmission converge to mediate striatum-dependent behaviors, while maladaptations in striatal circuitry contribute to mental disorders. However, the crosstalk between glutamate and dopamine signaling has not been entirely elucidated. Here we uncover a molecular mechanism by which glutamatergic and dopaminergic signaling integrate to regulate cAMP-dependent protein kinase (PKA) via phosphorylation of the PKA regulatory subunit, RIIβ. Using a combination of biochemical, pharmacological, neurophysiological, and behavioral approaches, we find that glutamate-dependent reduction in cyclin-dependent kinase 5 (Cdk5)-dependent RIIβ phosphorylation alters the PKA holoenzyme autoinhibitory state to increase PKA signaling in response to dopamine. Furthermore, we show that disruption of RIIβ phosphorylation by Cdk5 enhances cortico-ventral striatal synaptic plasticity. In addition, we demonstrate that acute and chronic stress in rats inversely modulate RIIβ phosphorylation and ventral striatal infusion of a small interfering peptide that selectively targets RIIβ regulation by Cdk5 improves behavioral response to stress. We propose this new signaling mechanism integrating ventral striatal glutamate and dopamine neurotransmission is important to brain function, may contribute to neuropsychiatric conditions, and serves as a possible target for the development of novel therapeutics for stress-related disorders.

Computational investigation of the dynamic control of cAMP signaling by PDE4 isoform types

Cyclic adenosine monophosphate (cAMP) is a generic signaling molecule that, through precise control of its signaling dynamics, exerts distinct cellular effects. Consequently, aberrant cAMP signaling can have detrimental effects. Phosphodiesterase 4 (PDE4) enzymes profoundly control cAMP signaling and comprise different isoform types of which the enzymatic activity is modulated by differential feedback mechanisms. Because these feedback dynamics are non-linear and occur coincidentally, their effects are difficult to examine experimentally, but can be well simulated computationally. Through understanding the role of PDE4 isoform types in regulating cAMP signaling, PDE4-targeted therapeutic strategies can be better specified. Here, we established a computational model to study how feedback mechanisms on different PDE4 isoform types lead to dynamic, isoform-specific control of cAMP signaling. Ordinary differential equations describing cAMP dynamics were implemented in the VirtualCell (VCell) environment. Simulations indicated that long PDE4 isoforms exert the most profound control on oscillatory cAMP signaling, as opposed to the PDE4-mediated control of single cAMP input pulses. Moreover, elevating cAMP levels or decreasing PDE4 levels revealed different effects on downstream signaling. Together these results underline that cAMP signaling is distinctly regulated by different PDE4 isoform types and that this isoform-specificity should be considered in both computational and experimental follow-up studies to better define PDE4 enzymes as therapeutic targets in diseases in which cAMP signaling is aberrant.

Can biophysical models of dendritic spines be used to explore synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction on society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive excitatory input, of spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of the dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during withdrawal, as well as during neurodegenerative disease progression such as Alzheimer's disease.

LRRK2 at Striatal Synapses: Cell-Type Specificity and Mechanistic Insights

Mutations in leucine-rich repeat kinase 2 (LRRK2) cause Parkinson’s disease with a similar clinical presentation and progression to idiopathic Parkinson’s disease, and common variation is linked to disease risk. Recapitulation of the genotype in rodent models causes abnormal dopamine release and increases the susceptibility of dopaminergic neurons to insults, making LRRK2 a valuable model for understanding the pathobiology of Parkinson’s disease. It is also a promising druggable target with targeted therapies currently in development. LRRK2 mRNA and protein expression in the brain is highly variable across regions and cellular identities. A growing body of work has demonstrated that pathogenic LRRK2 mutations disrupt striatal synapses before the onset of overt neurodegeneration. Several substrates and interactors of LRRK2 have been identified to potentially mediate these pre-neurodegenerative changes in a cell-type-specific manner. This review discusses the effects of pathogenic LRRK2 mutations in striatal neurons, including cell-type-specific and pathway-specific alterations. It also highlights several LRRK2 effectors that could mediate the alterations to striatal function, including Rabs and protein kinase A. The lessons learned from improving our understanding of the pathogenic effects of LRRK2 mutations in striatal neurons will be applicable to both dissecting the cell-type specificity of LRRK2 function in the transcriptionally diverse subtypes of dopaminergic neurons and also increasing our understanding of basal ganglia development and biology. Finally, it will inform the development of therapeutics for Parkinson’s disease.

Compartmentalized Signaling in Aging and Neurodegeneration

The cyclic AMP (cAMP) signalling cascade is necessary for cell homeostasis and plays important roles in many processes. This is particularly relevant during ageing and age-related diseases, where drastic changes, generally decreases, in cAMP levels have been associated with the progressive decline in overall cell function and, eventually, the loss of cellular integrity. The functional relevance of reduced cAMP is clearly supported by the finding that increases in cAMP levels can reverse some of the effects of ageing. Nevertheless, despite these observations, the molecular mechanisms underlying the dysregulation of cAMP signalling in ageing are not well understood. Compartmentalization is widely accepted as the modality through which cAMP achieves its functional specificity; therefore, it is important to understand whether and how this mechanism is affected during ageing and to define which is its contribution to this process. Several animal models demonstrate the importance of specific cAMP signalling components in ageing, however, how age-related changes in each of these elements affect the compartmentalization of the cAMP pathway is largely unknown. In this review, we explore the connection of single components of the cAMP signalling cascade to ageing and age-related diseases whilst elaborating the literature in the context of cAMP signalling compartmentalization.

Simplified calcium signaling cascade for synaptic plasticity

We propose a model for synaptic plasticity based on a calcium signaling cascade. The model simplifies the full signaling pathways from a calcium influx to the phosphorylation (potentiation) and dephosphorylation (depression) of glutamate receptors that are gated by fictive C1 and C2 catalysts, respectively. This model is based on tangible chemical reactions, including fictive catalysts, for long-term plasticity rather than the conceptual theories commonplace in various models, such as preset thresholds of calcium concentration. Our simplified model successfully reproduced the experimental synaptic plasticity induced by different protocols such as (i) a synchronous pairing protocol and (ii) correlated presynaptic and postsynaptic action potentials (APs). Further, the ocular dominance plasticity (or the experimental verification of the celebrated Bienenstock-Cooper-Munro theory) was reproduced by two model synapses that compete by means of back-propagating APs (bAPs). The key to this competition is synapse-specific bAPs with reference to bAP-boosting on the physiological grounds.

Geometric Control of Frequency Modulation of cAMP Oscillations due to Calcium in Dendritic Spines

The spatiotemporal regulation of cyclic adenosine monophosphate (cAMP) and its dynamic interactions with other second messengers such as calcium are critical features of signaling specificity required for neuronal development and connectivity. cAMP is known to contribute to long-term potentiation and memory formation by controlling the formation and regulation of dendritic spines. Despite the recent advances in biosensing techniques for monitoring spatiotemporal cAMP dynamics, the underlying molecular mechanisms that attribute to the subcellular modulation of cAMP remain unknown. In this work, we model the spatiotemporal dynamics of calcium-induced cAMP signaling pathway in dendritic spines. Using a three-dimensional reaction-diffusion model, we investigate the effect of different spatial characteristics of cAMP dynamics that may be responsible for subcellular regulation of cAMP concentrations. Our model predicts that the volume/surface ratio of the spine, regulated through the spine head size, spine neck size, and the presence of physical barriers (spine apparatus), is an important regulator of cAMP dynamics. Furthermore, localization of the enzymes responsible for the synthesis and degradation of cAMP in different compartments also modulates the oscillatory patterns of cAMP through exponential relationships. Our findings shed light on the significance of complex geometric and localization relationships for cAMP dynamics in dendritic spines.

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

Genetically Encoded Fluorescent Biosensors Illuminate the Spatiotemporal Regulation of Signaling Networks

Cellular signaling networks are the foundation which determines the fate and function of cells as they respond to various cues and stimuli. The discovery of fluorescent proteins over 25 years ago enabled the development of a diverse array of genetically encodable fluorescent biosensors that are capable of measuring the spatiotemporal dynamics of signal transduction pathways in live cells. In an effort to encapsulate the breadth over which fluorescent biosensors have expanded, we endeavored to assemble a comprehensive list of published engineered biosensors, and we discuss many of the molecular designs utilized in their development. Then, we review how the high temporal and spatial resolution afforded by fluorescent biosensors has aided our understanding of the spatiotemporal regulation of signaling networks at the cellular and subcellular level. Finally, we highlight some emerging areas of research in both biosensor design and applications that are on the forefront of biosensor development.

Competitive Tuning Among Ca2+/Calmodulin-Dependent Proteins: Analysis of in silico Model Robustness and Parameter Variability

Introduction

Calcium/Calmodulin-dependent (Ca²⁺/CaM-dependent) regulation of protein signaling has long been recognized for its importance in a number of physiological contexts. Found in almost all eukaryotic cells, Ca²⁺/CaM-dependent signaling participates in muscle development, immune responses, cardiac myocyte function and regulation of neuronal connectivity. In excitatory neurons, dynamic changes in the strength of synaptic connections, known as synaptic plasticity, occur when calcium ions (Ca²⁺) flux through NMDA receptors and bind the Ca²⁺-sensor calmodulin (CaM). Ca²⁺/CaM, in turn, regulates downstream protein signaling in actin polymerization, receptor trafficking, and transcription factor activation.The activation of downstream Ca²⁺/CaM-dependent binding proteins (CBPs) is a function of the frequency of Ca²⁺ flux, such that each CBP is preferentially "tuned" to different Ca²⁺ input signals. We have recently reported that competition among CBPs for CaM binding is alone sufficient to recreate in silico the observed in vivo frequency-dependence of several CBPs. However, CBP activation may strongly depend on the identity and concentration of proteins that constitute the competitive pool; with important implications in the regulation of CBPs in both normal and disease states.

Methods

Here, we extend our previous deterministic model of competition among CBPs to include phosphodiesterases, AMPAR receptors that are important in synaptic plasticity, and enzymatic function of CBPs: cAMP regulation, kinase activity, and phosphatase activity. After rigorous parameterization and validation by global sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC), we explore how perturbing the competitive pool of CBPs influences downstream signaling events. In particular, we hypothesize that although perturbations may decrease activation of one CBP, increased activation of a separate, but enzymatically-related CBP could compensate for this loss, providing a homeostatic effect.

Results and Conclusions

First we compare dynamic model output of two models: a two-state model of Ca²⁺/CaM binding and a four-state model of Ca²⁺/CaM binding. We find that a four-state model of Ca²⁺/CaM binding best captures the dynamic nature of the rapid response of CaM and CBPs to Ca²⁺ flux in the system. Using global sensitivity analysis, we find that model output is robust to parameter variability. Indeed, although variations in the expression of the CaM buffer neurogranin (Ng) may cause a decrease in Ca²⁺/CaM-dependent kinase II (CaMKII) activation, overall AMPA receptor phosphorylation is preserved; ostensibly by a concomitant increase in adenylyl cyclase 8 (AC8)-mediated activation of protein kinase A (PKA). Indeed phosphorylation of AMPAR receptors by CaMKII and PKA is robust across a wide range of Ng concentrations, though increases in AMPAR phosphorylation is seen at low Ng levels approaching zero. Our results may explain recent counter-intuitive results in neurogranin knockout mice and provide further evidence that competitive tuning is an important mechanism in synaptic plasticity. These results may be readily translated to other Ca²⁺/CaM-dependent signaling systems in other cell types and can be used to suggest targeted experimental investigation to explain counter-intuitive or unexpected downstream signaling outcomes.Tamara Kinzer-Ursem is an Assistant Professor in the Weldon School of Biomedical Engineering. She received her B.S. in Bioengineering from the University of Toledo and her M.S. and Ph.D. degrees in Chemical Engineering from the University of Michigan, and her post-doctoral training in Molecular Neuroscience at the California Institute of Technology. Prior to joining Purdue she was the Head of R&D in Biochemistry at Maven Biotechnologies and Visiting Associate in Chemical Engineering at the California Institute of Technology.Research in the Kinzer-Ursem lab focuses on developing tools to advance quantitative descriptions of cellular processes and disease within three areas of expertise: 1) Using particle diffusivity measurements to quantify biomolecular processes. Particle diffusometry is being used as a sensitive biosensor to detect the presence of pathogens in environmental and patient samples. 2) Development of novel protein tagging technologies that are used to label proteins in vivo to enable quantitative description of protein function and elucidate disease mechanisms. 3) Computational modeling of signal transduction mechanisms to understand cellular processes. Using computational techniques, we have recently described "competitive tuning" as a mechanism that might be used to regulate information transfer through protein networks, with implications in cell behavior and drug target analysis.

Molecular mechanisms underlying striatal synaptic plasticity: relevance to chronic alcohol consumption and seeking

The striatum, the input structure of the basal ganglia, is a major site of learning and memory for goal-directed actions and habit formation. Spiny projection neurons of the striatum integrate cortical, thalamic, and nigral inputs to learn associations, with cortico-striatal synaptic plasticity as a learning mechanism. Signaling molecules implicated in synaptic plasticity are altered in alcohol withdrawal, which may contribute to overly strong learning and increased alcohol seeking and consumption. To understand how interactions among signaling molecules produce synaptic plasticity, we implemented a mechanistic model of signaling pathways activated by dopamine D1 receptors, acetylcholine receptors, and glutamate. We use our novel, computationally efficient simulator, NeuroRD, to simulate stochastic interactions both within and between dendritic spines. Dopamine release during theta burst and 20-Hz stimulation was extrapolated from fast-scan cyclic voltammetry data collected in mouse striatal slices. Our results show that the combined activity of several key plasticity molecules correctly predicts the occurrence of either LTP, LTD, or no plasticity for numerous experimental protocols. To investigate spatial interactions, we stimulate two spines, either adjacent or separated on a 20-μm dendritic segment. Our results show that molecules underlying LTP exhibit spatial specificity, whereas 2-arachidonoylglycerol exhibits a spatially diffuse elevation. We also implement changes in NMDA receptors, adenylyl cyclase, and G protein signaling that have been measured following chronic alcohol treatment. Simulations under these conditions suggest that the molecular changes can predict changes in synaptic plasticity, thereby accounting for some aspects of alcohol use disorder.

Regulation of Nociceptive Plasticity Threshold and DARPP-32 Phosphorylation in Spinal Dorsal Horn Neurons by Convergent Dopamine and Glutamate Inputs

Dopamine can influence NMDA receptor function and regulate glutamate-triggered long-term changes in synaptic strength in several regions of the CNS. In spinal cord, regulation of the threshold of synaptic plasticity may determine the proneness to undergo sensitization and hyperresponsiveness to noxious input. In the current study, we increased endogenous dopamine levels in the dorsal horn by using re-uptake inhibitor GBR 12935. During the so-induced hyperdopaminergic transmission, conditioning low-frequency (1 Hz) stimulation (LFS) to the sciatic nerve induced long-term potentiation (LTP) of C-fiber-evoked potentials in dorsal horn neurons. The magnitude of LTP was attenuated by blockade of either dopamine D1-like receptors (D1LRs) by with SCH 23390 or NMDA receptor subunit NR2B with antagonist Ro25-6981. Conditioning LFS during GBR 12935 administration increased phosphorylation of dopamine- and cAMP-regulated phosphoprotein of Mr 32kDa (DARPP-32) at threonine 34 residue in synaptosomal (P3) fraction of dorsal horn homogenates, as assessed by Western blot analysis, which was partially prevented by NR2B blockade prior to conditioning stimulation. Conditioning LFS also was followed by higher co-localization of phosphorylated form of NR2B at tyrosine 1472 and pDARPP-32^Thr34- with postsynaptic marker PSD-95 in transverse L5 dorsal horn sections. Such increase could be significantly attenuated by D1LR blockade with SCH 23390. The current results support that coincidental endogenous recruitment of D1LRs and NR2B in dorsal horn synapses plays a role in regulating afferent-induced nociceptive plasticity. Parallel increases in DARPP-32 phosphorylation upon LTP induction suggests a role for this phosphoprotein as intracellular detector of convergent D1L- and NMDA receptor activation.

Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons

Transient changes in striatal dopamine (DA) concentration are considered to encode a reward prediction error (RPE) in reinforcement learning tasks. Often, a phasic DA change occurs concomitantly with a dip in striatal acetylcholine (ACh), whereas other neuromodulators, such as adenosine (Adn), change slowly. There are abundant adenylyl cyclase (AC) coupled GPCRs for these neuromodulators in striatal medium spiny neurons (MSNs), which play important roles in plasticity. However, little is known about the interaction between these neuromodulators via GPCRs. The interaction between these transient neuromodulator changes and the effect on cAMP/PKA signaling via Golf- and Gi/o-coupled GPCR are studied here using quantitative kinetic modeling. The simulations suggest that, under basal conditions, cAMP/PKA signaling could be significantly inhibited in D1R+ MSNs via ACh/M4R/Gi/o and an ACh dip is required to gate a subset of D1R/Golf-dependent PKA activation. Furthermore, the interaction between ACh dip and DA peak, via D1R and M4R, is synergistic. In a similar fashion, PKA signaling in D2+ MSNs is under basal inhibition via D2R/Gi/o and a DA dip leads to a PKA increase by disinhibiting A2aR/Golf, but D2+ MSNs could also respond to the DA peak via other intracellular pathways. This study highlights the similarity between the two types of MSNs in terms of high basal AC inhibition by Gi/o and the importance of interactions between Gi/o and Golf signaling, but at the same time predicts differences between them with regard to the sign of RPE responsible for PKA activation.

SIGNIFICANCE STATEMENT

Dopamine transients are considered to carry reward-related signal in reinforcement learning. An increase in dopamine concentration is associated with an unexpected reward or salient stimuli, whereas a decrease is produced by omission of an expected reward. Often dopamine transients are accompanied by other neuromodulatory signals, such as acetylcholine and adenosine. We highlight the importance of interaction between acetylcholine, dopamine, and adenosine signals via adenylyl-cyclase coupled GPCRs in shaping the dopamine-dependent cAMP/PKA signaling in striatal neurons. Specifically, a dopamine peak and an acetylcholine dip must interact, via D1 and M4 receptor, and a dopamine dip must interact with adenosine tone, via D2 and A2a receptor, in direct and indirect pathway neurons, respectively, to have any significant downstream PKA activation.

Development of computational models of cAMP signaling

Despite the growing evidence defining the cAMP signaling network as a master regulator of cellular function in a number of tissues, regulatory feedback loops, signal compartmentalization, as well as cross-talk with other signaling pathways make understanding the emergent properties of cAMP cellular action a daunting task. Dynamical models of signaling that combine quantitative rigor with molecular details can contribute valuable mechanistic insight into the complexity of intracellular cAMP signaling by complementing and guiding experimental efforts. In this chapter, we review the development of cAMP computational models. We describe how features of the cAMP network can be represented and review the types of experimental data useful in modeling cAMP signaling. We also compile a list of published cAMP models that can aid in the development of novel dynamical models of cAMP signaling.

Dendritic geometry shapes neuronal cAMP signalling to the nucleus

Neurons have complex dendritic trees, receiving numerous inputs at various distances from the cell body. Yet the rules of molecular signal propagation from dendrites to nuclei are unknown. DARPP-32 is a phosphorylation-regulated signalling hub in striatal output neurons. We combine diffusion-reaction modelling and live imaging to investigate cAMP-activated DARPP-32 signalling to the nucleus. The model predicts maximal effects on the nucleus of cAMP production in secondary dendrites, due to segmental decrease of dendrite diameter. Variations in branching, perikaryon size or spines have less pronounced effects. Biosensor kinase activity measurement following cAMP or dopamine uncaging confirms these predictions. Histone 3 phosphorylation, regulated by this pathway, is best stimulated by cAMP released in secondary-like dendrites. Thus, unexpectedly, the efficacy of diffusion-based signalling from dendrites to nucleus is not inversely proportional to the distance. We suggest a general mechanism by which dendritic geometry counterbalances the effect of dendritic distance for signalling to the nucleus.

Visualization of cyclic nucleotide dynamics in neurons

The second messengers cyclic adenosine monophosphate (cAMP) and cyclic guanosine monophosphate (cGMP) transduce many neuromodulatory signals from hormones and neurotransmitters into specific functional outputs. Their production, degradation and signaling are spatiotemporally regulated to achieve high specificity in signal transduction. The development of genetically encodable fluorescent biosensors has provided researchers with useful tools to study these versatile second messengers and their downstream effectors with unparalleled spatial and temporal resolution in cultured cells and living animals. In this review, we introduce the general design of these fluorescent biosensors and describe several of them in more detail. Then we discuss a few examples of using cyclic nucleotide fluorescent biosensors to study regulation of neuronal function and finish with a discussion of advances in the field. Although there has been significant progress made in understanding how the specific signaling of cyclic nucleotide second messengers is achieved, the mechanistic details in complex cell types like neurons are only just beginning to surface. Current and future fluorescent protein reporters will be essential to elucidate the role of cyclic nucleotide signaling dynamics in the functions of individual neurons and their networks.

4-Phenylbutyrate attenuates the ER stress response and cyclic AMP accumulation in DYT1 dystonia cell models

Dystonia is a neurological disorder in which sustained muscle contractions induce twisting and repetitive movements or abnormal posturing. DYT1 early-onset primary dystonia is the most common form of hereditary dystonia and is caused by deletion of a glutamic acid residue (302/303) near the carboxyl-terminus of encoded torsinA. TorsinA is localized primarily within the contiguous lumen of the endoplasmic reticulum (ER) and nuclear envelope (NE), and is hypothesized to function as a molecular chaperone and an important regulator of the ER stress-signaling pathway, but how the mutation in torsinA causes disease remains unclear. Multiple lines of evidence suggest that the clinical symptoms of dystonia result from abnormalities in dopamine (DA) signaling, and possibly involving its down-stream effector adenylate cyclase that produces the second messenger cyclic adenosine-3', 5'-monophosphate (cAMP). Here we find that mutation in torsinA induces ER stress, and inhibits the cyclic adenosine-3', 5'-monophosphate (cAMP) response to the adenylate cyclase agonist forskolin. Both defective mechanins are corrected by the small molecule 4-phenylbutyrate (4-PBA) that alleviates ER stress. Our results link torsinA, the ER-stress-response, and cAMP-dependent signaling, and suggest 4-PBA could also be used in dystonia treatment. Other pharmacological agents known to modulate the cAMP cascade, and ER stress may also be therapeutic in dystonia patients and can be tested in the models described here, thus supplementing current efforts centered on the dopamine pathway.

cAMP signaling microdomains and their observation by optical methods

The second messenger cyclic AMP (cAMP) is a major intracellular mediator of many hormones and neurotransmitters and regulates a myriad of cell functions, including synaptic plasticity in neurons. Whereas cAMP can freely diffuse in the cytosol, a growing body of evidence suggests the formation of cAMP gradients and microdomains near the sites of cAMP production, where cAMP signals remain apparently confined. The mechanisms responsible for the formation of such microdomains are subject of intensive investigation. The development of optical methods based on fluorescence resonance energy transfer (FRET), which allow a direct observation of cAMP signaling with high temporal and spatial resolution, is playing a fundamental role in elucidating the nature of such microdomains. Here, we will review the optical methods used for monitoring cAMP and protein kinase A (PKA) signaling in living cells, providing some examples of their application in neurons, and will discuss the major hypotheses on the formation of cAMP/PKA microdomains.

Systems biology of synaptic plasticity: a review on N-methyl-D-aspartate receptor mediated biochemical pathways and related mathematical models

Synaptic plasticity, an emergent property of synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we hope to discover the modulators and mechanisms that trigger memory formation. In this paper, we first review the well understood modulators and mechanisms underlying N-methyl-D-aspartate receptor dependent synaptic plasticity, a major form of synaptic plasticity in hippocampus, and then comment on the key mathematical modelling approaches available in the literature to understand synaptic plasticity as the integration of the established functionalities of synaptic components.

Mechanisms of dopamine D1 receptor-mediated ERK1/2 activation in the parkinsonian striatum and their modulation by metabotropic glutamate receptor type 5

In animal models of Parkinson's disease, striatal overactivation of ERK1/2 via dopamine (DA) D1 receptors is the hallmark of a supersensitive molecular response associated with dyskinetic behaviors. Here we investigate the pathways involved in D1 receptor-dependent ERK1/2 activation using acute striatal slices from rodents with unilateral 6-hydroxydopamine (6-OHDA) lesions. Application of the dopamine D1-like receptor agonist SKF38393 induced ERK1/2 phosphorylation and downstream signaling in the DA-denervated but not the intact striatum. This response was mediated through a canonical D1R/PKA/MEK1/2 pathway and independent of ionotropic glutamate receptors but blocked by antagonists of L-type calcium channels. Coapplication of an antagonist of metabotropic glutamate receptor type 5 (mGluR5) or its downstream signaling molecules (PLC, PKC, IP3 receptors) markedly attenuated SKF38393-induced ERK1/2 activation. The role of striatal mGluR5 in D1-dependent ERK1/2 activation was confirmed in vivo in 6-OHDA-lesioned animals treated systemically with SKF38393. In one experiment, local infusion of the mGluR5 antagonist MTEP in the DA-denervated rat striatum attenuated the activation of ERK1/2 signaling by SKF38393. In another experiment, 6-OHDA lesions were applied to transgenic mice with a cell-specific knockdown of mGluR5 in D1 receptor-expressing neurons. These mice showed a blunted striatal ERK1/2 activation in response to SFK38393 treatment. Our results reveal that D1-dependent ERK1/2 activation in the DA-denervated striatum depends on a complex interaction between PKA- and Ca(2+)-dependent signaling pathways that is critically modulated by striatal mGluR5.

LRRK2 regulates synaptogenesis and dopamine receptor activation through modulation of PKA activity

Leucine-rich repeat kinase 2 (LRRK2) is enriched in the striatal projection neurons (SPNs). We found that LRRK2 negatively regulates protein kinase A (PKA) activity in the SPNs during synaptogenesis and in response to dopamine receptor Drd1 activation. LRRK2 interacted with PKA regulatory subunit IIβ (PKARIIβ). A lack of LRRK2 promoted the synaptic translocation of PKA and increased PKA-mediated phosphorylation of actin-disassembling enzyme cofilin and glutamate receptor GluR1, resulting in abnormal synaptogenesis and transmission in the developing SPNs. Furthermore, PKA-dependent phosphorylation of GluR1 was also aberrantly enhanced in the striatum of young and aged Lrrk2(-/-) mice after treatment with a Drd1 agonist. Notably, a Parkinson's disease-related Lrrk2 R1441C missense mutation that impaired the interaction of LRRK2 with PKARIIβ also induced excessive PKA activity in the SPNs. Our findings reveal a previously unknown regulatory role for LRRK2 in PKA signaling and suggest a pathogenic mechanism of SPN dysfunction in Parkinson's disease.

Segregation and crosstalk of D1 receptor-mediated activation of ERK in striatal medium spiny neurons upon acute administration of psychostimulants

The convergence of corticostriatal glutamate and dopamine from the midbrain in the striatal medium spiny neurons (MSN) triggers synaptic plasticity that underlies reinforcement learning and pathological conditions such as psychostimulant addiction. The increase in striatal dopamine produced by the acute administration of psychostimulants has been found to activate not only effectors of the AC5/cAMP/PKA signaling cascade such as GluR1, but also effectors of the NMDAR/Ca(2+)/RAS cascade such as ERK. The dopamine-triggered effects on both these cascades are mediated by D1R coupled to Golf but while the phosphorylation of GluR1 is affected by reductions in the available amount of Golf but not of D1R, the activation of ERK follows the opposite pattern. This segregation is puzzling considering that D1R-induced Golf activation monotonically increases with DA and that there is crosstalk from the AC5/cAMP/PKA cascade to the NMDAR/Ca(2+)/RAS cascade via a STEP (a tyrosine phosphatase). In this work, we developed a signaling model which accounts for this segregation based on the assumption that a common pool of D1R and Golf is distributed in two D1R/Golf signaling compartments. This model integrates a relatively large amount of experimental data for neurons in vivo and in vitro. We used it to explore the crosstalk topologies under which the sensitivities of the AC5/cAMP/PKA signaling cascade to reductions in D1R or Golf are transferred or not to the activation of ERK. We found that the sequestration of STEP by its substrate ERK together with the insensitivity of STEP activity on targets upstream of ERK (i.e. Fyn and NR2B) to PKA phosphorylation are able to explain the experimentally observed segregation. This model provides a quantitative framework for simulation based experiments to study signaling required for long term potentiation in MSNs.

Modeling intracellular signaling underlying striatal function in health and disease

Striatum, which is the input nucleus of the basal ganglia, integrates cortical and thalamic glutamatergic inputs with dopaminergic afferents from the substantia nigra pars compacta. The combination of dopamine and glutamate strongly modulates molecular and cellular properties of striatal neurons and the strength of corticostriatal synapses. These actions are performed via intracellular signaling networks, containing several intertwined feedback loops. Understanding the role of dopamine and other neuromodulators requires the development of quantitative dynamical models for describing the intracellular signaling, in order to provide precise unambiguous descriptions and quantitative predictions. Building such models requires integration of data from multiple data sources containing information regarding the molecular interactions, the strength of these interactions, and the subcellular localization of the molecules. Due to the uncertainty, variability, and sparseness of these data, parameter estimation techniques are critical for inferring or constraining the unknown parameters, and sensitivity analysis evaluates which parameters are most critical for a given observed macroscopic behavior. Here, we briefly review the modeling approaches and tools that have been used to investigate biochemical signaling in the striatum, along with some of the models built around striatum. We also suggest a future direction for the development of such models from the, now becoming abundant, high-throughput data.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity

Interactions among signaling pathways that are activated by transmembrane receptors produce complex networks and emergent dynamical behaviors that are implicated in synaptic plasticity. Temporal dynamics and spatial aspects are critical determinants of cell responses such as synaptic plasticity, although the mapping between spatiotemporal activity pattern and direction of synaptic plasticity is not completely understood. Computational modeling of neuronal signaling pathways has significantly contributed to understanding signaling pathways underlying synaptic plasticity. Spatial models of signaling pathways in hippocampal neurons have revealed mechanisms underlying the spatial distribution of extracellular signal-related kinase (ERK) activation in hippocampal neurons. Other spatial models have demonstrated that the major role of anchoring proteins in striatal and hippocampal synaptic plasticity is to place molecules near their activators. Simulations of yet other models have revealed that the spatial distribution of synaptic plasticity may differ for potentiation versus depression. In general, the most significant advances have been made by interactive modeling and experiments; thus, an interdisciplinary approach should be applied to investigate critical issues in neuronal signaling pathways. These issues include identifying which transmembrane receptors are key for activating ERK in neurons, and the crucial targets of kinases that produce long-lasting synaptic plasticity. Although the number of computer programs for computationally efficient simulation of large reaction-diffusion networks is increasing, parameter estimation and sensitivity analysis in these spatial models remain more difficult than in single compartment models. Advances in live cell imaging coupled with further software development will continue to accelerate the development of spatial models of synaptic plasticity.

Spatial distribution of DARPP-32 in dendritic spines

The phosphoprotein DARPP-32 (dopamine and cyclic adenosine 3´, 5´-monophosphate-regulated phosphoprotein, 32 kDa) is an important component in the molecular regulation of postsynaptic signaling in neostriatum. Despite the importance of this phosphoprotein, there is as yet little known about the nanoscale distribution of DARPP-32. In this study we applied superresolution stimulated emission depletion microscopy (STED) to assess the expression and distribution of DARPP-32 in striatal neurons. Primary culture of striatal neurons were immunofluorescently labeled for DARPP-32 with Alexa-594 and for the dopamine D1 receptor (D1R) with atto-647N. Dual-color STED microscopy revealed discrete localizations of DARPP-32 and D1R in the spine structure, with clustered distributions in both head and neck. Dissected spine structures reveal that the DARPP-32 signal rarely overlapped with the D1R signal. The D1R receptor is positioned in an "aggregated" manner primarily in the spine head and to some extent in the neck, while DARPP-32 forms several neighboring small nanoclusters spanning the whole spine structure. The DARPP-32 clusters have a mean size of 52 +/- 6 nm, which is close to the resolution limit of the microscope and corresponds to the physical size of a few individual phosphoprotein immunocomplexes. Dissection of synaptic proteins using superresolution microscopy gives possibilities to reveal in better detail biologically relevant information, as compared to diffraction-limited microscopy. In this work, the dissected postsynaptic topology of the DARPP-32 phosphoprotein provides strong evidence for a compartmentalized and confined distribution in dendritic spines. The protein topology and the relatively low copy number of phosphoprotein provides a conception of DARPP-32's possibilities to fine-tune the regulation of synaptic signaling, which should have an impact on the performance of the neuronal circuits in which it is expressed.

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.

Dynamic modulation of spike timing-dependent calcium influx during corticostriatal upstates

The striatum of the basal ganglia demonstrates distinctive upstate and downstate membrane potential oscillations during slow-wave sleep and under anesthetic. The upstates generate calcium transients in the dendrites, and the amplitude of these calcium transients depends strongly on the timing of the action potential (AP) within the upstate. Calcium is essential for synaptic plasticity in the striatum, and these large calcium transients during the upstates may control which synapses undergo plastic changes. To investigate the mechanisms that underlie the relationship between calcium and AP timing, we have developed a realistic biophysical model of a medium spiny neuron (MSN). We have implemented sophisticated calcium dynamics including calcium diffusion, buffering, and pump extrusion, which accurately replicate published data. Using this model, we found that either the slow inactivation of dendritic sodium channels (NaSI) or the calcium inactivation of voltage-gated calcium channels (CDI) can cause high calcium corresponding to early APs and lower calcium corresponding to later APs. We found that only CDI can account for the experimental observation that sensitivity to AP timing is dependent on NMDA receptors. Additional simulations demonstrated a mechanism by which MSNs can dynamically modulate their sensitivity to AP timing and show that sensitivity to specifically timed pre- and postsynaptic pairings (as in spike timing-dependent plasticity protocols) is altered by the timing of the pairing within the upstate. These findings have implications for synaptic plasticity in vivo during sleep when the upstate-downstate pattern is prominent in the striatum.

Signaling pathways involved in striatal synaptic plasticity are sensitive to temporal pattern and exhibit spatial specificity

The basal ganglia is a brain region critically involved in reinforcement learning and motor control. Synaptic plasticity in the striatum of the basal ganglia is a cellular mechanism implicated in learning and neuronal information processing. Therefore, understanding how different spatio-temporal patterns of synaptic input select for different types of plasticity is key to understanding learning mechanisms. In striatal medium spiny projection neurons (MSPN), both long term potentiation (LTP) and long term depression (LTD) require an elevation in intracellular calcium concentration; however, it is unknown how the post-synaptic neuron discriminates between different patterns of calcium influx. Using computer modeling, we investigate the hypothesis that temporal pattern of stimulation can select for either endocannabinoid production (for LTD) or protein kinase C (PKC) activation (for LTP) in striatal MSPNs. We implement a stochastic model of the post-synaptic signaling pathways in a dendrite with one or more diffusionally coupled spines. The model is validated by comparison to experiments measuring endocannabinoid-dependent depolarization induced suppression of inhibition. Using the validated model, simulations demonstrate that theta burst stimulation, which produces LTP, increases the activation of PKC as compared to 20 Hz stimulation, which produces LTD. The model prediction that PKC activation is required for theta burst LTP is confirmed experimentally. Using the ratio of PKC to endocannabinoid production as an index of plasticity direction, model simulations demonstrate that LTP exhibits spine level spatial specificity, whereas LTD is more diffuse. These results suggest that spatio-temporal control of striatal information processing employs these Gq coupled pathways.

Transfer functions for protein signal transduction: application to a model of striatal neural plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.

The role of type 4 phosphodiesterases in generating microdomains of cAMP: large scale stochastic simulations

Cyclic AMP (cAMP) and its main effector Protein Kinase A (PKA) are critical for several aspects of neuronal function including synaptic plasticity. Specificity of synaptic plasticity requires that cAMP activates PKA in a highly localized manner despite the speed with which cAMP diffuses. Two mechanisms have been proposed to produce localized elevations in cAMP, known as microdomains: impeded diffusion, and high phosphodiesterase (PDE) activity. This paper investigates the mechanism of localized cAMP signaling using a computational model of the biochemical network in the HEK293 cell, which is a subset of pathways involved in PKA-dependent synaptic plasticity. This biochemical network includes cAMP production, PKA activation, and cAMP degradation by PDE activity. The model is implemented in NeuroRD: novel, computationally efficient, stochastic reaction-diffusion software, and is constrained by intracellular cAMP dynamics that were determined experimentally by real-time imaging using an Epac-based FRET sensor (H30). The model reproduces the high concentration cAMP microdomain in the submembrane region, distinct from the lower concentration of cAMP in the cytosol. Simulations further demonstrate that generation of the cAMP microdomain requires a pool of PDE4D anchored in the cytosol and also requires PKA-mediated phosphorylation of PDE4D which increases its activity. The microdomain does not require impeded diffusion of cAMP, confirming that barriers are not required for microdomains. The simulations reported here further demonstrate the utility of the new stochastic reaction-diffusion algorithm for exploring signaling pathways in spatially complex structures such as neurons.