Reinforcement learning theorizes that strengthening of synaptic connections in medium spiny neurons of the striatum occurs when glutamatergic input (from cortex) and dopaminergic input (from substantia nigra) are received simultaneously. Subsequent to learning, medium spiny neurons with strengthened synapses are more likely to fire in response to cortical input alone. This synaptic plasticity is produced by phosphorylation of AMPA receptors, caused by phosphorylation of various signalling molecules. A key signalling molecule is the phosphoprotein DARPP-32, highly expressed in striatal medium spiny neurons. DARPP-32 is regulated by several neurotransmitters through a complex network of intracellular signalling pathways involving cAMP (increased through dopamine stimulation) and calcium (increased through glutamate stimulation). Since DARPP-32 controls several kinases and phosphatases involved in striatal synaptic plasticity, understanding the interactions between cAMP and calcium, in particular the effect of transient stimuli on DARPP-32 phosphorylation, has major implications for understanding reinforcement learning. We developed a computer model of the biochemical reaction pathways involved in the phosphorylation of DARPP-32 on Thr34 and Thr75. Ordinary differential equations describing the biochemical reactions were implemented in a single compartment model using the software XPPAUT. Reaction rate constants were obtained from the biochemical literature. The first set of simulations using sustained elevations of dopamine and calcium produced phosphorylation levels of DARPP-32 similar to that measured experimentally, thereby validating the model. The second set of simulations, using the validated model, showed that transient dopamine elevations increased the phosphorylation of Thr34 as expected, but transient calcium elevations also increased the phosphorylation of Thr34, contrary to what is believed. When transient calcium and dopamine stimuli were paired, PKA activation and Thr34 phosphorylation increased compared with dopamine alone. This result, which is robust to variation in model parameters, supports reinforcement learning theories in which activity-dependent long-term synaptic plasticity requires paired glutamate and dopamine inputs.

Preface Synaptic plasticity is a mechanism proposed to underlie learning and memory. The complexity of the interactions between ion channels, enzymes, and genes involved in synaptic plasticity impedes a deep understanding of this phenomenon. Computer modeling is an approach to investigate the information processing that is performed by signaling pathways underlying synaptic plasticity. In the past few years, new software developments that blend computational neuroscience techniques with systems biology techniques have allowed large-scale, quantitative modeling of synaptic plasticity in neurons. We highlight significant advancements produced by these modeling efforts and introduce promising approaches that utilize advancements in live cell imaging.

Striatal fast-spiking (FS) interneurons are interconnected by gap junctions into sparsely connected networks. As demonstrated for cortical FS interneurons, these gap junctions in the striatum may cause synchronized spiking, which would increase the influence that FS neurons have on spiking by the striatal medium spiny (MS) neurons. Dysfunction of the basal ganglia is characterized by changes in synchrony or periodicity, thus gap junctions between FS interneurons may modulate synchrony and thereby influence behavior such as reward learning and motor control. To explore the roles of gap junctions on activity and spike synchronization in a striatal FS population, we built a network model of FS interneurons. Each FS connects to 30 -40% of its neighbors, as found experimentally, and each FS interneuron in the network is activated by simulated corticostriatal synaptic inputs. Our simulations show that the proportion of synchronous spikes in FS networks with gap junctions increases with increased conductance of the electrical synapse; however, the synchronization effects are moderate for experimentally estimated conductances. Instead, the main tendency is that the presence of gap junctions reduces the total number of spikes generated in response to synaptic inputs in the network. The reduction in spike firing is due to shunting through the gap junctions; which is minimized or absent when the neurons receive coincident inputs. Together these findings suggest that a population of electrically coupled FS interneurons may function collectively as input detectors that are especially sensitive to synchronized synaptic inputs received from the cortex.

Protein kinases play critical roles in learning and memory and in long term potentiation (LTP), a form of synaptic plasticity. The induction of late-phase LTP (L-LTP) in the CA1 region of the hippocampus requires several kinases, including CaMKII and PKA, which are activated by calcium-dependent signaling processes and other intracellular signaling pathways. The requirement for PKA is limited to L-LTP induced using spaced stimuli, but not massed stimuli. To investigate this temporal sensitivity of PKA, a computational biochemical model of L-LTP induction in CA1 pyramidal neurons was developed. The model describes the interactions of calcium and cAMP signaling pathways and is based on published biochemical measurements of two key synaptic signaling molecules, PKA and CaMKII. The model is stimulated using four 100 Hz tetani separated by 3 sec (massed) or 300 sec (spaced), identical to experimental L-LTP induction protocols. Simulations show that spaced stimulation activates more PKA than massed stimulation, and makes a key experimental prediction, that L-LTP is PKA-dependent for intervals larger than 60 sec. Experimental measurements of L-LTP demonstrate that intervals of 80 sec, but not 40 sec, produce PKA-dependent L-LTP, thereby confirming the model prediction. Examination of CaMKII reveals that its temporal sensitivity is opposite that of PKA, suggesting that PKA is required after spaced stimulation to compensate for a decrease in CaMKII. In addition to explaining the temporal sensitivity of PKA, these simulations suggest that the use of several kinases for memory storage allows each to respond optimally to different temporal patterns.

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

Long-term potentiation (LTP) of excitatory afferents to the dorsal striatum likely occurs with learning to encode new skills and habits, yet corticostriatal LTP is challenging to evoke reliably in brain slice under physiological conditions. Here we test the hypothesis that stimulating striatal afferents with theta-burst timing, similar to recently reported in vivo temporal patterns corresponding to learning, evokes LTP. Recording from adult mouse brain slice extracellularly in 1 mM Mg 2ϩ , we find LTP in dorsomedial and dorsolateral striatum is preferentially evoked by certain theta-burst patterns. In particular, we demonstrate that greater LTP is produced using moderate intraburst and high thetarange frequencies, and that pauses separating bursts of stimuli are critical for LTP induction. By altering temporal pattern alone, we illustrate the importance of burst-patterning for LTP induction and demonstrate that corticostriatal long-term depression is evoked in the same preparation. In accord with prior studies, LTP is greatest in dorsomedial striatum and relies on N-methyl-D-aspartate receptors. We also demonstrate a requirement for both G q -and G s/olf -coupled pathways, as well as several kinases associated with memory storage: PKC, PKA, and ERK. Our data build on previous reports of activitydirected plasticity by identifying effective values for distinct temporal parameters in variants of theta-burst LTP induction paradigms. We conclude that those variants which best match reports of striatal activity during learning behavior are most successful in evoking dorsal striatal LTP in adult brain slice without altering artificial cerebrospinal fluid. Future application of this approach will enable diverse investigations of plasticity serving striatal-based learning.

Signalling pathways leading to post-synaptic plasticity have been examined in many types of experimental studies, but a unified picture on how multiple biochemical pathways collectively shape neocortical plasticity is missing. We built a biochemically detailed model of post-synaptic plasticity describing CaMKII, PKA, and PKC pathways and their contribution to synaptic potentiation or depression. We developed a statistical AMPA-receptor-tetramer model, which permits the estimation of the AMPA-receptor-mediated maximal synaptic conductance based on numbers of GluR1s and GluR2s predicted by the biochemical signalling model. We show that our model reproduces neuromodulator-gated spike-timing-dependent plasticity as observed in the visual cortex and can be fit to data from many cortical areas, uncovering the biochemical contributions of the pathways pinpointed by the underlying experimental studies. Our model explains the dependence of different forms of plasticity on the availability of different proteins and can be used for the study of mental disorder-associated impairments of cortical plasticity.

Dopamine release in the striatum has been implicated in various forms of reward dependent learning. Dopamine leads to production of cAMP and activation of protein kinase A (PKA), which are involved in striatal synaptic plasticity and learning. PKA and its protein targets are not diffusely located throughout the neuron, but are confined to various subcellular compartments by anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Experiments have shown that blocking the interaction of PKA with AKAPs disrupts its subcellular location and prevents LTP in the hippocampus and striatum; however, these experiments have not revealed whether the critical function of anchoring is to locate PKA near the cAMP that activates it or near its targets, such as AMPA receptors located in the post-synaptic density. We have developed a large scale stochastic reaction-diffusion model of signaling pathways in a medium spiny projection neuron dendrite with spines, based on published biochemical measurements, to investigate this question and to evaluate whether dopamine signaling exhibits spatial specificity post-synaptically. The model was stimulated with dopamine pulses mimicking those recorded in response to reward. Simulations show that PKA colocalization with adenylate cyclase, either in the spine head or in the dendrite, leads to greater phosphorylation of DARPP-32 Thr34 and AMPA receptor GluA1 Ser845 than when PKA is anchored away from adenylate cyclase. Simulations further demonstrate that though cAMP exhibits a strong spatial gradient, diffusible DARPP-32 facilitates the spread of PKA activity, suggesting that additional inactivation mechanisms are required to produce spatial specificity of PKA activity.