Lobe Specific Ca2+-Calmodulin Nano-Domain in Neuronal Spines: A Single Molecule Level Analysis

Calmodulin (CaM) is a ubiquitous Ca2+ buffer and second messenger that affects cellular function as diverse as cardiac excitability, synaptic plasticity, and gene transcription. In CA1 pyramidal neurons, CaM regulates two opposing Ca2+-dependent processes that underlie memory formation: long-term potentiation (LTP) and long-term depression (LTD). Induction of LTP and LTD require activation of Ca2+-CaM-dependent enzymes: Ca2+/CaM-dependent kinase II (CaMKII) and calcineurin, respectively. Yet, it remains unclear as to how Ca2+ and CaM produce these two opposing effects, LTP and LTD. CaM binds 4 Ca2+ ions: two in its N-terminal lobe and two in its C-terminal lobe. Experimental studies have shown that the N- and C-terminal lobes of CaM have different binding kinetics toward Ca2+ and its downstream targets. This may suggest that each lobe of CaM differentially responds to Ca2+ signal patterns. Here, we use a novel event-driven particle-based Monte Carlo simulation and statistical point pattern analysis to explore the spatial and temporal dynamics of lobe-specific Ca2+-CaM interaction at the single molecule level. We show that the N-lobe of CaM, but not the C-lobe, exhibits a nano-scale domain of activation that is highly sensitive to the location of Ca2+ channels, and to the microscopic injection rate of Ca2+ ions. We also demonstrate that Ca2+ saturation takes place via two different pathways depending on the Ca2+ injection rate, one dominated by the N-terminal lobe, and the other one by the C-terminal lobe. Taken together, these results suggest that the two lobes of CaM function as distinct Ca2+ sensors that can differentially transduce Ca2+ influx to downstream targets. We discuss a possible role of the N-terminal lobe-specific Ca2+-CaM nano-domain in CaMKII activation required for the induction of synaptic plasticity

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors

Rapid Redistribution of Synaptic PSD-95 in the Neocortex In Vivo

Most excitatory synapses terminate on dendritic spines. Spines vary in size, and their volumes are proportional to the area of the postsynaptic density (PSD) and synaptic strength. PSD-95 is an abundant multi-domain postsynaptic scaffolding protein that clusters glutamate receptors and organizes the associated signaling complexes. PSD-95 is thought to determine the size and strength of synapses. Although spines and their synapses can persist for months in vivo, PSD-95 and other PSD proteins have shorter half-lives in vitro, on the order of hours. To probe the mechanisms underlying synapse stability, we measured the dynamics of synaptic PSD-95 clusters in vivo. Using two-photon microscopy, we imaged PSD-95 tagged with GFP in layer 2/3 dendrites in the developing (postnatal day 10–21) barrel cortex. A subset of PSD-95 clusters was stable for days. Using two-photon photoactivation of PSD-95 tagged with photoactivatable GFP (paGFP), we measured the time over which PSD-95 molecules were retained in individual spines. Synaptic PSD-95 turned over rapidly (median retention times τ (r) ~ 22–63 min from P10–P21) and exchanged with PSD-95 in neighboring spines by diffusion. PSDs therefore share a dynamic pool of PSD-95. Large PSDs in large spines captured more diffusing PSD-95 and also retained PSD-95 longer than small PSDs. Changes in the sizes of individual PSDs over days were associated with concomitant changes in PSD-95 retention times. Furthermore, retention times increased with developmental age (τ (r) ~ 100 min at postnatal day 70) and decreased dramatically following sensory deprivation. Our data suggest that individual PSDs compete for PSD-95 and that the kinetic interactions between PSD molecules and PSDs are tuned to regulate PSD size

Calcium Messenger Heterogeneity: A Possible Signal for Spike Timing-Dependent Plasticity

Calcium concentrations as well as time courses have been used to model the signaling cascades leading to changes in the strength of synaptic connections. Previous models consider the dendritic spines as uniform compartments regarding calcium signaling. However, calcium concentrations can vary drastically on distances much smaller than typical spine sizes, and downstream targets of calcium signals are often found exactly in these calcium nanodomains. Even though most downstream targets are activated by calcium via calmodulin, which is a diffusive molecule, the capacity of calmodulin to bind to its targets even when it is not fully loaded with calcium allows its downstream cascade to be highly local. In this study, a model is proposed which uses the heterogeneity of calcium concentrations as a signal for spike-timing-dependent plasticity (STDP). The model is minimalistic and includes three sources of calcium in spines: NMDA receptors (NMDARs), voltage gated calcium channels (VGCCs) and IP3 receptors (IP3Rs). It is based on the biochemical cascades and assumption of spatial locations of four calcium-dependent enzymes: calcium/calmodulin-dependent protein kinase II located near NMDARs, calcineurin located near VGCCs, cyclic nucleotide phosphodiesterase (PDE) located near IP3Rs or NMDARs and adenylyl cyclase, located between VDCCs and NMDARs. To quantify the changes in synaptic weights the model also includes a simple description of AMPA receptor insertion in the membrane and docking to the postsynaptic density. Two parameters of the model are tuned such that weight changes produced by either pre or postsynaptic firing alone are minimal. The model reproduces the typical shape of STDP for spike doublets. If PDE is located near IP3Rs, the behavior for spike triplets is consistent with that observed in hippocampal cell culture; if near NMDAR, the behavior is similar to that observed in cortical L2/3 slices

Synapse Geometry and Receptor Dynamics Modulate Synaptic Strength

Synaptic transmission relies on several processes, such as the location of a released vesicle, the number and type of receptors, trafficking between the postsynaptic density (PSD) and extrasynaptic compartment, as well as the synapse organization. To study the impact of these parameters on excitatory synaptic transmission, we present a computational model for the fast AMPA-receptor mediated synaptic current. We show that in addition to the vesicular release probability, due to variations in their release locations and the AMPAR distribution, the postsynaptic current amplitude has a large variance, making a synapse an intrinsic unreliable device. We use our model to examine our experimental data recorded from CA1 mice hippocampal slices to study the differences between mEPSC and evoked EPSC variance. The synaptic current but not the coefficient of variation is maximal when the active zone where vesicles are released is apposed to the PSD. Moreover, we find that for certain type of synapses, receptor trafficking can affect the magnitude of synaptic depression. Finally, we demonstrate that perisynaptic microdomains located outside the PSD impacts synaptic transmission by regulating the number of desensitized receptors and their trafficking to the PSD. We conclude that geometrical modifications, reorganization of the PSD or perisynaptic microdomains modulate synaptic strength, as the mechanisms underlying long-term plasticity

Engineering Approaches for Neurobiology

Neurobiological systems span a wide dimensional range. We present a scale-driven methodological development for three biological systems to demonstrate the utility of applied engineering approaches in neurobiology and provide an avenue for future study. Concepts in computational modeling, microfluidic device platforms, and MRI phantoms are examined - starting from the level of a single synapse and concluding with long-distance cortical connectivity.Single synapse models were developed using a Monte Carlo simulation environment to study biophysically realistic mechanisms of spike timing dependent plasticity (STDP). A model of spatiotemporal intracellular Calcium detection was extended to include subunit-specific receptor kinetics and distributions. Using STDP-based activation protocols, global and local molecular time courses were then produced for NR2a and NR2b knockout models. To study network level oscillatory activity, a model of spatially-constrained networks was created based on cyclic geometry to look at the effects of circumference and track-width on spontaneous network activity. Transverse wave activity is demonstrated and characterized by velocity and origin. Microfluidic technology provides an experimental means to extend the study of network organization and activity in vitro. We have developed a microfluidic control platform that integrates multiple design strategies to address the intrinsic spatiotemporal resolution of neurons. Microfluidic devices were fabricated using multilayer soft-lithography with internal valves to guide multiple laminar streams. A control platform using dynamic pressure produces a targeted hydrodynamic stream from variable internal resistance control. Feedback containing video and pressure data provides online analysis of the microfluidic device. Devices were characterized with arbitrary profile generation, profile repeatability, flow rate measurement, and lid-driven flow production. Finally, a microfluidic phantom for diffusion-weighted magnetic resonance imaging was developed for validation studies of long-distance cortical white matter connections. The diffusion phantom provides a reliable physical structure with which high resolution fiber tractography methods can be tested against. The diffusion phantom was fabricated using conventional photolithographic techniques with an internal channel network that mimics white matter fiber tracts and crossings. We show mapped tracts to the features inside of the phantom via post-processing of diffusion-weighted images

Subcellular Location of PKA Controls Striatal Plasticity: Stochastic Simulations in Spiny Dendrites

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

Mechanism underlying hippocampal long-term potentiation and depression based on competition between endocytosis and exocytosis of AMPA receptors

N-methyl-D-aspartate (NMDA) receptor-dependent long-term potentiation (LTP) and long-term depression (LTD) of signal transmission form neural circuits and thus are thought to underlie learning and memory. These mechanisms are mediated by AMPA receptor (AMPAR) trafficking in postsynaptic neurons. However, the regulatory mechanism of bidirectional plasticity at excitatory synapses remains unclear. We present a network model of AMPAR trafficking for adult hippocampal pyramidal neurons, which reproduces both LTP and LTD. We show that the induction of both LTP and LTD is regulated by the competition between exocytosis and endocytosis of AMPARs, which are mediated by the calcium-sensors synaptotagmin 1/7 (Syt1/7) and protein interacting with C-kinase 1 (PICK1), respectively. Our result indicates that recycling endosomes containing AMPAR are always ready for Syt1/7-dependent exocytosis of AMPAR at peri-synaptic/synaptic membranes. This is because molecular motor myosin V-b constitutively transports the recycling endosome toward the membrane in a Ca2+-independent manner

The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover

Molecular switches have been implicated in the storage of information in biological systems. For small structures such as synapses, these switches are composed of only a few molecules and stochastic fluctuations are therefore of importance. Such fluctuations could potentially lead to spontaneous switch reset that would limit the lifetime of information storage. We have analyzed a model of the calcium/calmodulin-dependent protein kinase II (CaMKII) switch implicated in long-term memory in the nervous system. The bistability of this switch arises from autocatalytic autophosphorylation of CaMKII, a reaction that is countered by a saturable phosphatase-1-mediated dephosphorylation. We sought to understand the factors that control switch stability and to determine the functional relationship between stability and the number of molecules involved. Using Monte Carlo simulations, we found that the lifetime of states of the switch increase exponentially with the number of CaMKII holoenzymes. Switch stability requires a balance between the kinase and phosphatase rates, and the kinase rate must remain high relative to the rate of protein turnover. Thus, a critical limit on switch stability is set by the observed turnover rate (one per 30 h on average). Our computational results show that, depending on the timescale of fluctuations in enzyme numbers, for a switch composed of about 15 CaMKII holoenzymes, the stable persistent activation can span from a few years to a human lifetime