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

Multi-Stage Modeling of the Kinetics of Activation of CaMKII

Ca 2+ /calmodulin-dependent protein kinase 2 (CaMKII) plays an important role in induction of long-term potentiation and formation of memory. It is abundant in dendritic spines, and is activated when Ca 2+ flows into the postsynaptic cytosol through open NMDA-type glutamate receptors. Its function is fine-tuned through interaction with other proteins as well as through subunit interactions and regulatory autophosphorylation. We have undertaken a multi-stage project to study the critical kinetics of activation of CaMKII in the spine by combining modeling and experimental studies. We are using computational modeling and simulations on various platforms, coupled with biochemical experiments in vitro, and eventually in vivo, to understand CaMKII regulation. The project includes the following steps: 1. Determining the parameters governing activation of a monomeric subunit. The CaMKII holoenzyme is a large dodecamer of similar, homologous subunits held together by interactions between the association domains located at the carboxyl end of each subunit. Individual, monomeric subunits can be expressed recombinantly by removing the association domain. Computer simulations of activation of monomeric CaMKII by Ca 2+ /calmodulin at both saturating and non-saturating concentrations in a test tube have helped to identify the binding parameters that are most crucial for modeling of regulation of CaMKII and thus have indicated the most useful biochemical assays to measure those parameters (Pepke et al., 2010). We are using these measurements to fine-tune our model of activation of individual catalytic subunits. 2. Building a model of the holoenzyme. Because a CaMKII holoenzyme contains 12 similar subunits, each of which can exist in several states, the holoenzyme can have a large number of state combinations. Thus, modeling the entire holoenzyme requires a computational framework that avoids the ensuing combinatorial complexity. The stochastic simulator MCell provides an elegant, rule-based way of modeling state changes in the CaMKII holoenzyme. 3. Modeling cooperativity that arises from the dodecameric structure of CaMKII. Autophosphorylation at threonine-286, which activates CaMKII subunits, is an inter-subunit event. Thus, it is greatly facilitated by the close proximity of subunits in the holoenzyme. In addition, the subunits within the holoenzyme are arranged as dimers which appears to result in cooperativity in the binding of Ca 2+ /CaM to individual subunits of the dimer (Chao et al., 2010). An accurate model of activation of subunits in the holoenzyme and their autophosphorylation will allow us to explore the effects of cooperativity on CaMKII activation on various time scales. 4. Modeling CaMKII within the context of a postsynaptic spine CaMKII interacts with a variety of other proteins, both in the postsynaptic density (PSD), close to major sources of Ca 2+ influx, and in other parts of the spine. In the fourth stage of this project we plan to implement kinetic models of activation of CaMKII in the context of an MCell model of Ca 2+ influx into a spine upon activation of NMDA-type glutamate receptors (Keller et al., 2008; Keller et al., 2011, submitted). We will explore the effects of different localization and numbers of CaMKII holoenzymes in the spine on CaMKII activation. References: Pepke, S., Kinzer-Ursem, T., Mihalas, S., and Kennedy, M.B. (2010). A dynamic model of interactions of Ca 2+ , calmodulin, and catalytic subunits of Ca 2+ /calmodulin-dependent protein kinase II. PLoS Comput Biol 6, e1000675. Chao, L.H., Pellicena, P., Deindl, S., Barclay, L.A., Schulman, H., and Kuriyan, J. (2010). Intersubunit capture of regulatory segments is a component of cooperative CaMKII activation. Nat Struct Mol Biol 17, 264-272. Keller, D.X., Franks, K.M., Bartol, T.M., Jr., and Sejnowski, T.J. (2008). Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines. PLoS ONE 3, e2045. Keller, D.X., Bartol, T.M., Kinney, J.P, Kennedy, M.B., Bajaj, C., Harris, K.M., and Sejnowski, T.J. Regulation of synaptic calcium transients in reconstructed dendritic spines of hippocampal CA1 pyramidal neurons, submitted

A general theory of intertemporal decision-making and the perception of time

Animals and humans make decisions based on their expected outcomes. Since relevant outcomes are often delayed, perceiving delays and choosing between earlier versus later rewards (intertemporal decision-making) is an essential component of animal behavior. The myriad observations made in experiments studying intertemporal decision-making and time perception have not yet been rationalized within a single theory. Here we present a theory-Training--Integrated Maximized Estimation of Reinforcement Rate (TIMERR)--that explains a wide variety of behavioral observations made in intertemporal decision-making and the perception of time. Our theory postulates that animals make intertemporal choices to optimize expected reward rates over a limited temporal window; this window includes a past integration interval (over which experienced reward rate is estimated) and the expected delay to future reward. Using this theory, we derive a mathematical expression for the subjective representation of time. A unique contribution of our work is in finding that the past integration interval directly determines the steepness of temporal discounting and the nonlinearity of time perception. In so doing, our theory provides a single framework to understand both intertemporal decision-making and time perception.Comment: 37 pages, 4 main figures, 3 supplementary figure

A Computational Analysis of the Function of Three Inhibitory Cell Types in Contextual Visual Processing

Most cortical inhibitory cell types exclusively express one of three genes, parvalbumin, somatostatin and 5HT3a. The visual responses of cortical neurons are affected not only by local cues, but also by visual context. As the inhibitory neuron types have distinctive synaptic sources and targets over different spatial extents and from different areas, we conjecture that they possess distinct roles in contextual processing. We use modeling to relate structural information to function in primary visual cortex (V1) of the mouse, and investigate their role in contextual visual processing. Our findings are threefold. First, the inhibition mediated by parvalbumin positive (PV) cells mediates local processing and could underlie their role in boundary detection. Second, the inhibition mediated by somatostatin-positive (SST) cells facilitates longer range spatial competition among receptive fields. Third, non-specific top-down modulation to interneurons expressing vasoactive intestinal polypeptide (VIP), a subclass of 5HT3a neurons, can selectively enhance V1 responses.Comment: 39 pages, 5 figures, 4 supplemental figures, 2 table

Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data

Recent advances in neuroscientific experimental techniques have enabled us to simultaneously record the activity of thousands of neurons across multiple brain regions. This has led to a growing need for computational tools capable of analyzing how task-relevant information is represented and communicated between several brain regions. Partial information decompositions (PIDs) have emerged as one such tool, quantifying how much unique, redundant and synergistic information two or more brain regions carry about a task-relevant message. However, computing PIDs is computationally challenging in practice, and statistical issues such as the bias and variance of estimates remain largely unexplored. In this paper, we propose a new method for efficiently computing and estimating a PID definition on multivariate Gaussian distributions. We show empirically that our method satisfies an intuitive additivity property, and recovers the ground truth in a battery of canonical examples, even at high dimensionality. We also propose and evaluate, for the first time, a method to correct the bias in PID estimates at finite sample sizes. Finally, we demonstrate that our Gaussian PID effectively characterizes inter-areal interactions in the mouse brain, revealing higher redundancy between visual areas when a stimulus is behaviorally relevant

Effects of Chronic Sleep Restriction during Early Adolescence on the Adult Pattern of Connectivity of Mouse Secondary Motor Cortex

Cortical circuits mature in stages, from early synaptogenesis and synaptic pruning to late synaptic refinement, resulting in the adult anatomical connection matrix. Because the mature matrix is largely fixed, genetic or environmental factors interfering with its establishment can have irreversible effects. Sleep disruption is rarely considered among those factors, and previous studies have focused on very young animals and the acute effects of sleep deprivation on neuronal morphology and cortical plasticity. Adolescence is a sensitive time for brain remodeling, yet whether chronic sleep restriction (CSR) during adolescence has long-term effects on brain connectivity remains unclear. We used viral-mediated axonal labeling and serial two-photon tomography to measure brain-wide projections from secondary motor cortex (MOs), a high-order area with diffuse projections. For each MOs target, we calculated the projection fraction, a combined measure of passing fibers and axonal terminals normalized for the size of each target. We found no homogeneous differences in MOs projection fraction between mice subjected to 5 days of CSR during early adolescence (P25–P30, ≥50% decrease in daily sleep, n=14) and siblings that slept undisturbed (n=14). Machine learning algorithms, however, classified animals at significantly above chance levels, indicating that differences between the two groups exist, but are subtle and heterogeneous. Thus, sleep disruption in early adolescence may affect adult brain connectivity. However, because our method relies on a global measure of projection density and was not previously used to measure connectivity changes due to behavioral manipulations, definitive conclusions on the long-term structural effects of early CSR require additional experiments

Widespread presence of direction-reversing neurons in the mouse visual system

Direction selectivity, the preference of motion in one direction over the opposite, is a fundamental property of visual neurons across species. We find that a substantial proportion of direction selective neurons in the mouse visual system reverse their preferred direction of motion in response to drifting gratings at different spatiotemporal parameters. A spatiotemporally asymmetric filter model recapitulates our experimental observations