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1.  Protein Crowding within the Postsynaptic Density Can Impede the Escape of Membrane Proteins 
The Journal of Neuroscience  2016;36(15):4276-4295.
Mechanisms regulating lateral diffusion and positioning of glutamate receptors within the postsynaptic density (PSD) determine excitatory synaptic strength. Scaffold proteins in the PSD are abundant receptor binding partners, yet electron microscopy suggests that the PSD is highly crowded, potentially restricting the diffusion of receptors regardless of binding. However, the contribution of macromolecular crowding to receptor retention remains poorly understood. We combined experimental and computational approaches to test the effect of synaptic crowding on receptor movement and positioning in Sprague Dawley rat hippocampal neurons. We modeled AMPA receptor diffusion in synapses where the distribution of scaffold proteins was determined from photoactivated localization microscopy experiments, and receptor–scaffold association and dissociation rates were adjusted to fit single-molecule tracking and fluorescence recovery measurements. Simulations predicted that variation of receptor size strongly influences the fractional synaptic area the receptor may traverse, and the proportion that may exchange in and out of the synapse. To test the model experimentally, we designed a set of novel transmembrane (TM) probes. A single-pass TM protein with one PDZ binding motif concentrated in the synapse as do AMPARs yet was more mobile there than the much larger AMPAR. Furthermore, either the single binding motif or an increase in cytoplasmic bulk through addition of a single GFP slowed synaptic movement of a small TM protein. These results suggest that both crowding and binding limit escape of AMPARs from the synapse. Moreover, tight protein packing within the PSD may modulate the synaptic dwell time of many TM proteins important for synaptic function.
SIGNIFICANCE STATEMENT Small alterations to the distribution within synapses of key transmembrane proteins, such as receptors, can dramatically change synaptic strength. Indeed, many diseases are thought to unbalance neural circuit function in this manner. Processes that regulate this in healthy synapses are unclear, however. By combining computer simulations with imaging methods that examined protein dynamics at multiple scales in space and time, we showed that both steric effects and protein–protein binding each regulate the mobility of receptors in the synapse. Our findings extend our knowledge of the synapse as a crowded environment that counteracts molecular diffusion, and support the idea that both molecular collisions and biochemical binding can be involved in the regulation of neural circuit performance.
PMCID: PMC4829651  PMID: 27076425
FRAP; GFP imaging; inducible dimerization; single-molecule tracking; stochastic modeling; uPAINT
2.  Biochemical principles underlying the stable maintenance of LTP by the CaMKII/NMDAR complex 
Brain research  2014;1621:51-61.
Memory involves the storage of information at synapses by an LTP-like process. This information storage is synapse specific and can endure for years despite the turnover of all synaptic proteins. There must, therefore, be special principles that underlie the stability of LTP. Recent experimental results suggest that LTP is maintained by the complex of CaMKII with the NMDAR. Here we consider the specifics of the CaMKII/NMDAR molecular switch, with the goal of understanding the biochemical principles that underlie stable information storage by synapses. Consideration of a variety of experimental results suggests that multiple principles are involved. One switch requirement is to prevent spontaneous transitions from the off to the on state. The highly cooperative nature of CaMKII autophosphorylation by Ca2+ (Hill coefficient of 8) and the fact that formation of the CaMKII/NMDAR complex requires release of CaMKII from actin are mechanisms that stabilize the off state. The stability of the on state depends critically on intersubunit autophosphorylation, a process that restores any loss of pT286 due to phosphatase activity. Intersubunit autophosphorylation is also important in explaining why on state stability is not compromised by protein turnover. Recent evidence suggests that turnover occurs by subunit exchange. Thus, stability could be achieved if a newly inserted unphosphorylated subunit was autophosphorylated by a neighboring subunit. Based on other recent work, we posit a novel mechanism that enhances the stability of the on state by protection of pT286 from phosphatases. We posit that the binding of the NMNDAR to CaMKII forces pT286 into the catalytic site of a neighboring subunit, thereby protecting pT286 from phosphatases. A final principle concerns the role of structural changes. The binding of CaMKII to the NMDAR may act as a tag to organize the binding of further proteins that produce the synapse enlargement that underlies late LTP. We argue that these structural changes not only enhance transmission, but also enhance the stability of the CaMKII/NMDAR complex. Together, these principles provide a mechanistic framework for understanding how individual synapses produce stable information storage.
PMCID: PMC4466085  PMID: 25511992
Memory; LTP; Kinase; Phosphatase
3.  Dendritic spine geometry can localize GTPase signaling in neurons 
Molecular Biology of the Cell  2015;26(22):4171-4181.
The spread of Cdc42 activation at dendritic spines is modeled by means of reaction-diffusion equations solved on spine-like geometries. Excitable behavior arising from positive feedback in Cdc42 activation leads to traveling waves of Cdc42 activity. The narrow neck of the dendritic spine halts wave propagation, resulting in localized Cdc42 signaling.
Dendritic spines are the postsynaptic terminals of most excitatory synapses in the mammalian brain. Learning and memory are associated with long-lasting structural remodeling of dendritic spines through an actin-mediated process regulated by the Rho-family GTPases RhoA, Rac, and Cdc42. These GTPases undergo sustained activation after synaptic stimulation, but whereas Rho activity can spread from the stimulated spine, Cdc42 activity remains localized to the stimulated spine. Because Cdc42 itself diffuses rapidly in and out of the spine, the basis for the retention of Cdc42 activity in the stimulated spine long after synaptic stimulation has ceased is unclear. Here we model the spread of Cdc42 activation at dendritic spines by means of reaction-diffusion equations solved on spine-like geometries. Excitable behavior arising from positive feedback in Cdc42 activation leads to spreading waves of Cdc42 activity. However, because of the very narrow neck of the dendritic spine, wave propagation is halted through a phenomenon we term geometrical wave-pinning. We show that this can account for the localization of Cdc42 activity in the stimulated spine, and, of interest, retention is enhanced by high diffusivity of Cdc42. Our findings are broadly applicable to other instances of signaling in extreme geometries, including filopodia and primary cilia.
PMCID: PMC4710246  PMID: 26337387
4.  Mechanisms of CaMKII action in long-term potentiation 
Nature reviews. Neuroscience  2012;13(3):169-182.
Long-term potentiation (LTP) of synaptic strength occurs during learning and can last for long periods, making it a probable mechanism for memory storage. LTP induction results in calcium entry, which activates calcium–calmodulin-dependent protein kinase II (CaMKII). CaMKII subsequently translocates to the synapse, where it binds to the NMDA-type glutamate receptors and produces potentiation by phosphorylating principal and auxiliary subunits of AMPA-type glutamate receptors. These processes all are localized to stimulated spines and account for the synapse specificity of LTP. In the later stages of LTP, CaMKII has a structural role in enlarging and strengthening the synapse.
PMCID: PMC4050655  PMID: 22334212
5.  Nanoscale scaffolding domains within the postsynaptic density concentrate synaptic AMPA receptors 
Neuron  2013;78(4):615-622.
Scaffolding molecules at the postsynaptic membrane form the foundation of excitatory synaptic transmission by establishing the architecture of the postsynaptic density (PSD), but the small size of the synapse has precluded measurement of PSD organization in live cells. We measured the internal structure of the PSD in live neurons at approximately 25 nm resolution using photoactivated localization microscopy (PALM). We found that four major PSD scaffold molecules are each organized in distinctive nanodomains ~80 nm in diameter, intrasynaptic protein ensembles that undergo striking changes over time. Further, the dense subdomains of PSD-95 were preferentially enriched in AMPA receptors more than NMDA receptors. Chronic suppression of activity triggered changes in PSD interior architecture that may help amplify synaptic plasticity. The observed clustered architecture of the PSD controlled the amplitude and variance of simulated postsynaptic currents, suggesting several ways in which PSD interior organization may regulate the strength and plasticity of neurotransmission.
PMCID: PMC3668352  PMID: 23719161
6.  Neurons in posterior cingulate cortex signal exploratory decisions in a dynamic multi-option choice task 
Current biology : CB  2009;19(18):1532-1537.
In dynamic environments, adaptive behavior requires striking a balance between harvesting currently available rewards (exploitation) and gathering information about alternative options (exploration) [1–4]. Such strategic decisions should incorporate not only recent reward history, but also opportunity costs and environmental statistics. Previous neuroimaging [5–8] and neurophysiological [9–13] studies have implicated several brain areas, including orbitofrontal cortex, anterior cingulate cortex, and ventral striatum, in distinguishing between bouts of exploration and exploitation. Nonetheless, the neuronal mechanisms that underlie selection between these strategies remain poorly understood. We hypothesized that posterior cingulate cortex (CGp), an area linking reward processing, attention [14], memory [15, 16], and motor control systems [17], mediates the integration of decision variables such as reward [18], uncertainty [19], and target location [20] that underlie the dynamic balance of exploration and exploitation. Here we show that CGp neurons distinguish between exploratory and exploitative decisions made by monkeys in a dynamic foraging task. Moreover, the firing rates of these neurons predict in graded fashion the strategy most likely to be selected on upcoming trials. This encoding is distinct from mere switching between spatial targets, and is independent of the absolute magnitudes of rewards. These observations implicate CGp in both the integration of individual outcomes across decision making and the modification of strategy in dynamic environments.
PMCID: PMC3515083  PMID: 19733074
7.  Quantitative estimates of the cytoplasmic, PSD, and NMDAR-bound pools of CaMKII in dendritic spines 
Brain research  2011;1419:46-52.
CaMKII plays a critical role in long-term potentiation (LTP). The kinase is a major component of the postsynaptic density (PSD); however, it is also contained in the spine cytoplasm. CaMKII can now be monitored optically in living neurons, and it is therefore important to understand the contribution of the PSD and cytoplasmic pools to optical signals. Here, we estimate the size of these pools under basal conditions. From EM immunolabeling data, we calculate that the PSD/cytoplasmic ratio is ~5%. A second independent estimate is derived from measurements indicating that the average mushroom spine PSD contains 90 to 240 holoenzymes. A cytoplasmic concentration of 16 µM (~2590 holoenzymes) in the spine can be estimated from the total measured CaMKII content of hippocampal tissue, the relative volume of different compartments, and the spine-dendrite ratio of CaMKII (2:1). These numbers yield a second estimate (6%) of the PSD/spine ratio in good agreement with the first. The CaMKII bound to the NMDAR is important because preventing the formation of this complex blocks LTP induction. We estimate that the percentage of spine CaMKII held active by binding to the NMDAR is ~0.2%. Implications of the high spine concentration of CaMKII (> 100 micromolar alpha subunits) and the small fraction within the PSD are discussed. Of particular note, the finding that the CaMKII signal in spines shows only transient activation (open state) after LTP induction is subject to the qualification that it does not reflect the small but important pool bound to the NMDAR.
PMCID: PMC3196057  PMID: 21925648
Ca2+/calmodulin-dependent protein Kinase II; postsynaptic density; spine; calmodulin; actin
8.  Quantifying Negative Feedback Regulation by micro-RNAs 
Physical biology  2011;8(5):055002.
Micro-RNAs (miRNAs) play a crucial role in post-transcriptional gene regulation by pairing with target mRNAs to repress protein production. It has been shown that over one-third of human genes are targeted by miRNA. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. In this study, we explore the functional roles of feedback regulation by miRNAs. In a model where repression of translation occurs by sequestration of mRNA by miRNA, we find that miRNA and mRNA levels are anti-correlated, resulting in larger fluctuation in protein levels than theoretically expected assuming no correlation between miRNA and mRNA levels. If miRNA repression is due to a catalytic suppression of translation rates, we analytically show that the protein fluctuations can be strongly repressed with miRNA regulation. We also discuss how either of these modes may be relevant for cell function.
PMCID: PMC3184398  PMID: 21832809
microRNA; negative feedback regulation; sequestration model; mean field theory; kinetic suppression model; linear noise approximation
9.  Calmodulin as a Direct Detector of Ca2+ Signals 
Nature neuroscience  2011;14(3):301-304.
Many forms of signal transduction occur when Ca2+ enters the cytoplasm of a cell. It has been generally thought that there is a fast buffer that rapidly reduces the free Ca2+ level and that it is this buffered level of Ca2+ that triggers downstream biochemical processes, notably the activation of calmodulin (CaM) and the resulting activation of CaM-dependent enzymes. Given the importance of these transduction processes, it is critical to understand exactly how Ca2+ triggers CaM. We have determined the rate at which Ca2+ binds to calmodulin (CaM) and found that Ca2+ binds more rapidly than to other Ca2+-binding proteins. This property of CaM and its high concentration argue for a new view of signal transduction: CaM directly intercepts incoming Ca2+ and sets the free Ca2+ levels (i.e., strongly contributes to fast Ca2+ buffering) rather than responding to the lower Ca2+ level set by other buffers. This property is critical for making CaM an efficient transducer. Our results also suggest a new role for other Ca2+ binding proteins (CBPs) in regulating the lifetime of Ca2+ bound to CaM, thereby setting the gain of signal transduction.
PMCID: PMC3057387  PMID: 21258328
11.  Quantifying the Effects of Elastic Collisions and Non-Covalent Binding on Glutamate Receptor Trafficking in the Post-Synaptic Density 
PLoS Computational Biology  2010;6(5):e1000780.
One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.
Author Summary
One of the most accepted theories of information storage in neurons is that it is partially localized in the strength of synaptic contacts. Evidence suggests that at the cellular level, in combination with other cellular mechanisms, this is implemented by increasing or decreasing the concentration of a particular type of membrane molecules. Two opposing mechanisms have to coexist in synapses to allow them to store information. On one hand, synapses have to be flexible, to allow the storage of new memories. On the other hand, synapses have to be stable to preserve previously learned information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which molecules can enter, leave and remain in the synapse are unclear. Our modeling work uses fundamental biophysical principles to quantify the effects of molecular collisions and biochemical reactions. Our results show that molecular collisions alone, between the diffusing proteins with anchored molecules in the synapse, can replicate known experimental results. Molecular collision in combination with biochemical binding can be fundamental biophysical principles used by synapses for the formation and preservation of memories.
PMCID: PMC2869312  PMID: 20485563
12.  A Physiologically-Inspired Model of Numerical Classification Based on Graded Stimulus Coding 
In most natural decision contexts, the process of selecting among competing actions takes place in the presence of informative, but potentially ambiguous, stimuli. Decisions about magnitudes – quantities like time, length, and brightness that are linearly ordered – constitute an important subclass of such decisions. It has long been known that perceptual judgments about such quantities obey Weber's Law, wherein the just-noticeable difference in a magnitude is proportional to the magnitude itself. Current physiologically inspired models of numerical classification assume discriminations are made via a labeled line code of neurons selectively tuned for numerosity, a pattern observed in the firing rates of neurons in the ventral intraparietal area (VIP) of the macaque. By contrast, neurons in the contiguous lateral intraparietal area (LIP) signal numerosity in a graded fashion, suggesting the possibility that numerical classification could be achieved in the absence of neurons tuned for number. Here, we consider the performance of a decision model based on this analog coding scheme in a paradigmatic discrimination task – numerosity bisection. We demonstrate that a basic two-neuron classifier model, derived from experimentally measured monotonic responses of LIP neurons, is sufficient to reproduce the numerosity bisection behavior of monkeys, and that the threshold of the classifier can be set by reward maximization via a simple learning rule. In addition, our model predicts deviations from Weber Law scaling of choice behavior at high numerosity. Together, these results suggest both a generic neuronal framework for magnitude-based decisions and a role for reward contingency in the classification of such stimuli.
PMCID: PMC2814553  PMID: 20126432
LIP; number; signal detection; decision making; reinforcement learning; neuroeconomics; discrimination
13.  The Effects of NR2 Subunit-Dependent NMDA Receptor Kinetics on Synaptic Transmission and CaMKII Activation 
PLoS Computational Biology  2008;4(10):e1000208.
N-Methyl-d-aspartic acid (NMDA) receptors are widely expressed in the brain and are critical for many forms of synaptic plasticity. Subtypes of the NMDA receptor NR2 subunit are differentially expressed during development; in the forebrain, the NR2B receptor is dominant early in development, and later both NR2A and NR2B are expressed. In heterologous expression systems, NR2A-containing receptors open more reliably and show much faster opening and closing kinetics than do NR2B-containing receptors. However, conflicting data, showing similar open probabilities, exist for receptors expressed in neurons. Similarly, studies of synaptic plasticity have produced divergent results, with some showing that only NR2A-containing receptors can drive long-term potentiation and others showing that either subtype is capable of driving potentiation. In order to address these conflicting results as well as open questions about the number and location of functional receptors in the synapse, we constructed a Monte Carlo model of glutamate release, diffusion, and binding to NMDA receptors and of receptor opening and closing as well as a model of the activation of calcium-calmodulin kinase II, an enzyme critical for induction of synaptic plasticity, by NMDA receptor-mediated calcium influx. Our results suggest that the conflicting data concerning receptor open probabilities can be resolved, with NR2A- and NR2B-containing receptors having very different opening probabilities. They also support the conclusion that receptors containing either subtype can drive long-term potentiation. We also are able to estimate the number of functional receptors at a synapse from experimental data. Finally, in our models, the opening of NR2B-containing receptors is highly dependent on the location of the receptor relative to the site of glutamate release whereas the opening of NR2A-containing receptors is not. These results help to clarify the previous findings and suggest future experiments to address open questions concerning NMDA receptor function.
Author Summary
Information processing in the brain is carried out by networks of neurons connected by synapses. Synapses can change strength, allowing these networks to adapt and learn, in a process known as synaptic plasticity. At a synapse, an electrical signal in one neuron is converted into a chemical signal, carried by a neurotransmitter, which is in turn converted into electrical and chemical signals in another neuron by specialized proteins called receptors. One such protein, the N-methyl-d-aspartic acid (NMDA) receptor, is particularly important for plasticity, due to its ability to detect the voltage of the cell receiving the neurotransmitter signal and to the fact that it allows calcium, an important signaling molecule, to enter the cell. Here we use computational modeling to investigate the role of one part of the NMDA receptor: the NR2 subunit. The subunit has various forms, and which of these forms are present in the NMDA receptor can strongly affect the kinetics and other properties of the receptor. We show that, along with changing the kinetics of the receptor, changing the NR2 subunit affects the reliability of the receptor, its ability to respond to large stimuli, and its spatial response properties. These results have implications for synaptic transmission and plasticity.
PMCID: PMC2563690  PMID: 18974824

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