Geometric principles of second messenger dynamics in dendritic spines.

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity

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

Hydrodynamic Fin Function of Brief Squid, Lolliguncula Brevis

Although the pulsed jet is often considered the foundation of a squid\u27s locomotive system, the lateral fins also probably play an important role in swimming, potentially providing thrust, lift and dynamic stability as needed. Fin morphology and movement vary greatly among squid species, but the locomotive role of the fins is not well understood. To begin to elucidate the locomotive role of the fins in squids, fin hydrodynamics were studied in the brief squid Lolliguncula brevis, a species that exhibits a wide range of fin movements depending on swimming speed. Individual squid were trained to swim in both the arms-first and tail-first orientations against currents in a water tunnel seeded with light-reflective particles. Particle-laden water around the fins was illuminated with lasers and videotaped so that flow dynamics around the fins could be analyzed using digital particle image velocimetry (DPIV). Time-averaged forces generated by the fin were quantified from vorticity fields of the fin wake. During the low swimming speeds considered in this study [\u3c2.5 dorsal mantle lengths (DML) per second], L. brevis exhibited four unique fin wake patterns, each with distinctive vortical structures: (1) fin mode I, in which one vortex is shed with each downstroke, generally occurring at low speeds; (2) fin mode II, an undulatory mode in which a continuous linked chain of vortices is produced; (3) fin mode III, in which one vortex is shed with each downstroke and upstroke, and; (4) fin mode IV, in which a discontinuous chain of linked double vortex structures is produced. All modes were detected during tail-first swimming but only fin modes II and III were observed during arms-first swimming. The fins produced horizontal and vertical forces of varying degrees depending on stroke phase, swimming speed, and swimming orientation. During tail-first swimming, the fins functioned primarily as stabilizers at low speeds before shifting to propulsors as speed increased, all while generating net lift. During arms-first swimming, the fins primarily provided lift with thrust production playing a reduced role. These results demonstrate the lateral fins are an integral component of the complex locomotive system of L. brevis, producing lift and thrust forces through different locomotive modes

Swimming Dynamics and Propulsive Efficiency of Squids Throughout Ontogeny

Synopsis Squids encounter vastly different flow regimes throughout ontogeny as they undergo critical morphological changes to their two locomotive systems: the fins and jet. Squid hatchlings (paralarvae) operate at low and intermediate Reynolds numbers (Re) and typically have rounded bodies, small fins, and relatively large funnel apertures whereas juveniles and adults operate at higher Re and generally have more streamlined bodies, larger fins, and relatively small funnel apertures. These morphological changes and varying flow conditions affect swimming performance in squids. To determine how swimming dynamics and propulsive efficiency change throughout ontogeny, digital particle image velocimetry (DPIV) and kinematic data were collected from an ontogenetic range of long-finned squid Doryteuthis pealeii and brief squid Lolliguncula brevis swimming in a holding chamber or water tunnel (Re=20-20 000). Jet and fin wake bulk properties were quantified, and propulsive efficiency was computed based on measurements of impulse and excess kinetic energy in the wakes. Paralarvae relied predominantly oil a vertically directed, high frequency, low velocity jet as they bobbed up and down in the water column. Although sonic spherical vortex rings were observed, most paralarval jets consisted of an elongated vertical region of variable length with no clear pinch-off of a vortex ring from the trailing tail component. Compared with paralarvae, juvenile and adult squid exhibited a more diverse range of swimming strategies, involving greater overall locomotive fin reliance and multiple fin and jet wake modes with better defined vortex rings. Despite greater locomotive flexibility, jet propulsive efficiency of juveniles/adults was significantly lower than that of paralarvae, even when juvenile/adults employed their highest efficiency jet mode involving the production of periodic isolated vortex rings with each jet pulse. When the fins were considered together with the jet for several juvenile/adult swimming sequences, overall propulsive efficiency increased, suggesting that fin contributions are important and Should not be overlooked in analyses of the swimming performance of squids. The fins produced significant thrust and consistently had higher propulsive efficiency than did the jet. One particularly important area of future Study is the determination of coordinated jet/fin wake modes that have the greatest impact oil propulsive efficiency. Although such research would be technically challenging, requiring new, powerful, 3D approaches, it is necessary for a more comprehensive assessment of propulsive efficiency of the squid dual-mode locomotive system

Hydrodynamics of Pulsed Jetting in Juvenile and Adult Brief Squid Lolliguncula Brevis: Evidence of Multiple Jet \u27Modes\u27 and Their Implications for Propulsive Efficiency

The dynamics of pulsed jetting in squids throughout ontogeny is not well understood, especially with regard to the development of vortex rings, which are common features of mechanically generated jet pulses (also known as starting jets). Studies of mechanically generated starting jets have revealed a limiting principle for vortex ring formation characterized in terms of a \u27formation number\u27 (F), which delineates the transition between the formation of isolated vortex rings and vortex rings that have \u27pinched off\u27 from the generating jet. Near F, there exists an optimum in pulse-averaged thrust with (potentially) low energetic cost, raising the question: do squids produce vortex rings and if so, do they fall near F, where propulsive benefits presumably occur? To better understand vortex ring dynamics and propulsive jet efficiency throughout ontogeny, brief squid Lolliguncula brevis ranging from 3.3 to 9.1 cm dorsal mantle length (DML) and swimming at speeds of 2.43-22.2cm s-1 (0.54-3.50 DML s-1) were studied using digital particle image velocimetry (DPIV). A range of jet structures were observed but most structures could be classified as variations of two principal jet modes: (1) jet mode I, where the ejected fluid rolled up into an isolated vortex ring; and (2) jet mode II, where the ejected fluid developed into a leading vortex ring that separated or \u27pinched off\u27 from a long trailing jet. The ratio of jet length [based on the vorticity extent (Lω] to jet diameter [based on peak vorticity locations (Dω] was \u3c3.0 for jet mode I and \u3e 3.0 for jet mode II, placing the transition between modes in rough agreement with F determined in mechanical jet studies. Jet mode II produced greater time-averaged thrust and lift forces and was the jet mode most heavily used whereas jet mode I had higher propulsive efficiency, lower slip, shorter jet periods and a higher frequency of fin activity associated with it. No relationship between Lω/Dω and speed was detected and there was no apparent speed preference for the jet modes within the speed range considered in this study; however, propulsive efficiency did increase with speed partly because of a reduction in slip and jet angle with speed. Trends in higher slip, lower propulsive efficiency and higher relative lift production were observed for squid \u3c5.0 cm DML compared with squid \u3e= 5.0 cm DML. While these trends were observed when jet mode I and II were equally represented among the size classes, there was also greater relative dependence on jet mode I than jet mode II for squid \u3c5.0 cm DML when all of the available jet sequences were examined. Collectively, these results indicate that similar to 5.0 cm DML is an important ontogenetic transition for the hydrodynamics of pulsed jetting in squids. The significance of our findings is that from early juvenile through to adult life stages, L. brevis is capable of producing a diversity of vortex ring-based jet structures, ranging from efficient short pulses to high-force longer duration pulses. Given that some of these structures had Lω/Dωs near F, and F represented the delineation between the two primary jet modes observed, fluid dynamics probably played an integral role in the evolution of squid locomotive systems. When this flexibility in jet dynamics is coupled with the highly versatile fins, which are capable of producing multiple hydrodynamic modes as well, it is clear that squid have a locomotive repertoire far more complex than orignally thought

Pulsed Jet Dynamics of Squid Hatchlings at Intermediate Reynolds Numbers

Squid paralarvae (hatchlings) rely predominantly on a pulsed jet for locomotion, distinguishing them from the majority of aquatic locomotors at low/intermediate Reynolds numbers (Re), which employ oscillatory/undulatory modes of propulsion. Although squid paralarvae may delineate the lower size limit of biological jet propulsion, surprisingly little is known about the hydrodynamics and propulsive efficiency of paralarval jetting within the intermediate Re realm. To better understand paralarval jet dynamics, we used digital particle image velocimetry (DPIV) and high-speed video to measure bulk vortex properties ( e. g. circulation, impulse, kinetic energy) and other jet features [ e. g. average and peak jet velocity along the jet centerline (Uj and Ujmax, respectively), jet angle, jet length based on the vorticity and velocity extents (Lω and LV, respectively), jet diameter based on the distance between vorticity peaks (Dω), maximum funnel diameter (DF), average and maximum swimming speed (U and Umax, respectively)] in free-swimming Doryteuthis pealeii paralarvae (1.8 mm dorsal mantle length) (Resquid=25-90). Squid paralarvae spent the majority of their time station holding in the water column, relying predominantly on a frequent, high-volume, vertically directed jet. During station holding, paralarvae produced a range of jet structures from spherical vortex rings ( Lω/Dω=2.1, LV/DF=13.6) to more elongated vortex ring structures with no distinguishable pinch-off (Lω/Dω= 4.6, LV/DF=36.0). To swim faster, paralarvae increased pulse duration and Lω/Dω, leading to higher impulse but kept jet velocity relatively constant. Paralarvae produced jets with low slip, i.e. ratio of jet velocity to swimming velocity (Uj/U or Ujmax/Umax), and exhibited propulsive efficiency [ηpd=74.9 +/- 8.83% (+/- s.d.) for deconvolved data] comparable with oscillatory/ undulatory swimmers. As slip decreased with speed, propulsive efficiency increased. The detection of high propulsive efficiency in paralarvae is significant because it contradicts many studies that predict low propulsive efficiency at intermediate Re for inertial forms of locomotion