Protein Crowding within the Postsynaptic Density Can Impede the Escape of Membrane Proteins.

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.

Mechanisms of CaMKII action in long-term potentiation.

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 NMDA-type glutamate receptors and produces potentiation by phosphorylating principal and auxiliary subunits of AMPA-type glutamate receptors. These processes are all 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.

Quantifying negative feedback regulation by micro-RNAs.

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.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density.

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.

The effects of NR2 subunit-dependent NMDA receptor kinetics on synaptic transmission and CaMKII activation.

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.

Model for a robust neural integrator.

Integrator circuits in the brain show persistent firing that reflects the sum of previous excitatory and inhibitory inputs from external sources. Integrator circuits have been implicated in parametric working memory, decision making and motor control. Previous work has shown that stable integrator function can be achieved by an excitatory recurrent neural circuit, provided synaptic strengths are tuned with extreme precision (better than 1% accuracy). Here we show that integrator circuits can function without fine tuning if the neuronal units have bistable properties. Two specific mechanisms of bistability are analyzed, one based on local recurrent excitation, and the other on the voltage-dependence of the NMDA (N-methyl-D-aspartate) channel. Neither circuit requires fine tuning to perform robust integration, and the latter actually exploits the variability of neuronal conductances.

A unified model of the presynaptic and postsynaptic changes during LTP at CA1 synapses.

Long-term potentiation (LTP) has been studied extensively at CA1 synapses of the hippocampus, and there is evidence implicating both postsynaptic and presynaptic changes in this process. These changes include (i) addition of AMPA channels to the extrasynaptic membrane and diffusional equilibrium of extrasynaptic receptors with synaptic receptors, (ii) sudden addition of AMPA channels to the synapse in large groups, (iii) a change in the mode of glutamate release (presumably from kiss-and-run to full fusion), and (iv) a delayed increase in the number of vesicles released. However, it remains unclear whether (or how) these changes work together. We have incorporated all of these processes into a structural model of the synapse. We propose that the synapse is composed of transsynaptic modules that function quasi-independently in AMPA-mediated transmission. Under basal conditions, synapses are partially silent; some modules are AMPA-silent (but contribute to NMDA-mediated transmission), whereas others are functional (and contribute to both AMPA- and NMDA-mediated transmission). During LTP, there is both a rapid change in the mode of vesicle fusion and a rapid insertion of a postsynaptic complex (a hyperslot) containing many proteins (slots) capable of binding AMPA channels. The combined effect of these pre- and postsynaptic changes is to convert AMPA-silent modules into functional modules. Slot filling is transiently enhanced by a rapid increase in extrasynaptic GluR1, a form of the AMPA-type receptor. A slower transsynaptic growth process adds AMPA-silent modules to the synapse, enhancing the number of vesicles released and thereby enhancing the NMDA response. This model accounts for a broad range of data, including the LTP-induced changes in quantal parameters. The model also provides a coherent explanation for the diverse effects of GluR1 knockout on basal transmission, LTP, and distance-dependent scaling.

Biochemical principles underlying the stable maintenance of LTP by the CaMKII/NMDAR complex.

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 Ca(2+) (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. This article is part of a Special Issue entitled SI: Brain and Memory.

Dendritic spine geometry can localize GTPase signaling in neurons.

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.

Simultaneous roles for Ca2+ in excitation and adaptation of Limulus ventral photoreceptors.

The ventral photoreceptors of Limulus have been one of the main preparations for the study of invertebrate phototransduction. The study of ventral photoreceptors has revealed that they have remarkable performance characteristics, most notably the very large amplification of the transduction process. This amplification is critically dependent upon the coupling of photoactivated rhodopsin to the phosphoinositide cascade, resulting in the release of Ca2+ from intracellular stores. The consequent elevation of Ca2+ within the photoreceptor's cytosol is amongst the most rapid and dramatic known to be activated by the phosphoinositide cascade. This review summarizes the evidence that intracellular Ca2+ is a key regulator of transduction in Limulus photoreceptors. The mechanisms that regulate Ca2+ as well as the possible targets of the action of Ca2+ are reviewed. Ca2+ elevation is critical for triggering both excitation and adaptation processes in the photoreceptor. The question of how a single second messenger can produce these two opposing effects is of obvious interest and is a topic dealt with throughout this review.

Nanoscale scaffolding domains within the postsynaptic density concentrate synaptic AMPA receptors.

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 proteins were each organized in distinctive ∼80 nm ensembles able to undergo striking changes over time. Bidirectional PALM and single-molecule immunolabeling showed that dense nanodomains 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.

Quantitative estimates of the cytoplasmic, PSD, and NMDAR-bound pools of CaMKII in dendritic spines.

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 µM 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.

Calmodulin as a direct detector of Ca2+ signals.

Many forms of signal transduction occur when Ca(2+) enters the cytoplasm of a cell. It has been generally thought that there is a fast buffer that rapidly reduces the free Ca(2+) level and that it is this buffered level of Ca(2+) 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 crucial to understand exactly how Ca(2+) activates CaM. We have determined the rate at which Ca(2+) binds to CaM and found that Ca(2+) binds more rapidly to CaM than to other Ca(2+)-binding proteins. This property of CaM and its high concentration support a new view of signal transduction: CaM directly intercepts incoming Ca(2+) and sets the free Ca(2+) level (that is, it strongly contributes to fast Ca(2+) buffering) rather than responding to the lower Ca(2+) level set by other buffers. This property is crucial for making CaM an efficient transducer. Our results also suggest that other Ca(2+) binding proteins have a previously undescribed role in regulating the lifetime of Ca(2+) bound to CaM and thereby setting the gain of signal transduction.

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.

Neurons in posterior cingulate cortex signal exploratory decisions in a dynamic multioption choice task.

In dynamic environments, adaptive behavior requires striking a balance between harvesting currently available rewards (exploitation) and gathering information about alternative options (exploration). Such strategic decisions should incorporate not only recent reward history, but also opportunity costs and environmental statistics. Previous neuroimaging and neurophysiological studies have implicated orbitofrontal cortex, anterior cingulate cortex, and ventral striatum in distinguishing between bouts of exploration and exploitation. Nonetheless, the neuronal mechanisms that underlie strategy selection remain poorly understood. We hypothesized that posterior cingulate cortex (CGp), an area linking reward processing, attention, memory, and motor control systems, mediates the integration of variables such as reward, uncertainty, and target location that underlie this dynamic balance. Here we show that CGp neurons distinguish between exploratory and exploitative decisions made by monkeys in a dynamic foraging task. Moreover, firing rates of these neurons predict in graded fashion the strategy most likely to be selected on upcoming trials. This encoding is distinct from switching between targets and is independent of the absolute magnitudes of rewards. These observations implicate CGp in the integration of individual outcomes across decision making and the modification of strategy in dynamic environments.

The sequence of events that underlie quantal transmission at central glutamatergic synapses.

The properties of synaptic transmission were first elucidated at the neuromuscular junction. More recent work has examined transmission at synapses within the brain. Here we review the remarkable progress in understanding the biophysical and molecular basis of the sequential steps in this process. These steps include the elevation of Ca2+ in microdomains of the presynaptic terminal, the diffusion of transmitter through the fusion pore into the synaptic cleft and the activation of postsynaptic receptors. The results give insight into the factors that control the precision of quantal transmission and provide a framework for understanding synaptic plasticity.

Properties of quantal transmission at CA1 synapses.

We have used Monte Carlo simulations to understand the generation of quantal responses at the single active zones of CA1 synapses. We constructed a model of AMPA channel activation that accounts for the responses to controlled glutamate application and a model of glutamate diffusion in the synaptic cleft. With no further adjustments to these models, we simulated the response to the release of glutamate from a single vesicle. The predicted response closely matches the rise time of observed responses, which recent measurements show is much faster (<100 micros) than previously thought. The simulations show that initial channel opening is driven by a brief (<100 micros) glutamate spike near the site of vesicle fusion, producing a hotspot of channel activation (diameter: approximately 250 nm) smaller than many synapses. Quantal size therefore depends more strongly on the density of channels than their number, a finding that has important implications for measuring synaptic strength. Recent measurements allow estimation of AMPA receptor density at CA1 synapses. Using this value, our simulations correctly predicts a quantal amplitude of approximately 10 pA. We have also analyzed the properties of excitatory postsynaptic currents (EPSCs) generated by the multivesicular release that can occur during evoked responses. We find that summation is nearly linear and that the existence of multiple narrow peaks in amplitude histograms can be accounted for. It has been unclear how to reconcile the existence of these narrow peaks, which indicate that the variation of quantal amplitude is small (CV < 0.2) with the highly variable amplitude of miniature EPSCs (mEPSCs; CV approximately 0.6). According to one theory, mEPSC variability arises from variation in vesicle glutamate content. However, both our modeling results and recent experimental results indicate that this view cannot account for the observed rise time/amplitude correlation of mEPSCs. In contrast, this correlation and the high mEPSC variability can be accounted for if some mEPSCs are generated by two or more vesicles released with small temporal jitter. We conclude that a broad range of results can be accounted for by simple principles: quantal amplitude (approximately 10 pA) is stereotyped, some mEPSCs are multivesicular at moderate and large synapses, and evoked responses are generated by quasi-linear summation of multiple quanta.

Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task.

An important question in neuroscience is whether and how temporal patterns and fluctuations in neuronal spike trains contribute to information processing in the cortex. We have addressed this issue in the memory-related circuits of the prefrontal cortex by analyzing spike trains from a database of 229 neurons recorded in the dorsolateral prefrontal cortex of 4 macaque monkeys during the performance of an oculomotor delayed-response task. For each task epoch, we have estimated their power spectrum together with interspike interval histograms and autocorrelograms. We find that 1). the properties of most (about 60%) neurons approximated the characteristics of a Poisson process. For about 25% of cells, with characteristics typical of interneurons, the power spectrum showed a trough at low frequencies (<20 Hz) and the autocorrelogram a dip near zero time lag. About 15% of neurons had a peak at <20 Hz in the power spectrum, associated with the burstiness of the spike train; 2). a small but significant task dependency of spike-train temporal structure: delay responses to preferred locations were characterized not only by elevated firing, but also by suppressed power at low (<20 Hz) frequencies; and 3). the variability of interspike intervals is typically higher during the mnemonic delay period than during the fixation period, regardless of the remembered cue. The high irregularity of neural persistent activity during the delay period is likely to be a characteristic signature of recurrent prefrontal network dynamics underlying working memory.