Paradoxical signaling regulates structural plasticity in dendritic spines

Transient spine enlargement (3-5 min timescale) is an important event associated with the structural plasticity of dendritic spines. Many of the molecular mechanisms associated with transient spine enlargement have been identified experimentally. Here, we use a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium-influx due to NMDA receptor activation. We have identified that a key feature of this signaling network is the paradoxical signaling loop. Paradoxical components act bifunctionally in signaling networks and their role is to control both the activation and inhibition of a desired response function (protein activity or spine volume). Using ordinary differential equation (ODE)-based modeling, we show that the dynamics of different regulators of transient spine expansion including CaMKII, RhoA, and Cdc42 and the spine volume can be described using paradoxical signaling loops. Our model is able to capture the experimentally observed dynamics of transient spine volume. Furthermore, we show that actin remodeling events provide a robustness to spine volume dynamics. We also generate experimentally testable predictions about the role of different components and parameters of the network on spine dynamics

Hotspots of dendritic spine turnover facilitate clustered spine addition and learning and memory.

Modeling studies suggest that clustered structural plasticity of dendritic spines is an efficient mechanism of information storage in cortical circuits. However, why new clustered spines occur in specific locations and how their formation relates to learning and memory (L&M) remain unclear. Using in vivo two-photon microscopy, we track spine dynamics in retrosplenial cortex before, during, and after two forms of episodic-like learning and find that spine turnover before learning predicts future L&M performance, as well as the localization and rates of spine clustering. Consistent with the idea that these measures are causally related, a genetic manipulation that enhances spine turnover also enhances both L&M and spine clustering. Biophysically inspired modeling suggests turnover increases clustering, network sparsity, and memory capacity. These results support a hotspot model where spine turnover is the driver for localization of clustered spine formation, which serves to modulate network function, thus influencing storage capacity and L&M

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

Shape manipulation using physically based wire deformations

This paper develops an efficient, physically based shape manipulation technique. It defines a 3D model with profile curves, and uses spine curves generated from the profile curves to control the motion and global shape of 3D models. Profile and spine curves are changed into profile and spine wires by specifying proper material and geometric properties together with external forces. The underlying physics is introduced to deform profile and spine wires through the closed form solution to ordinary differential equations for axial and bending deformations. With the proposed approach, global shape changes are achieved through manipulating spine wires, and local surface details are created by deforming profile wires. A number of examples are presented to demonstrate the applications of our proposed approach in shape manipulation

Stability of the human spine: a biomechanical study

The influences of curvatures and of physical properties on the mechanical stability of the spine were analysed by means of a three-dimensional, geometrical, nonlinear biomechanical model. According to the model, the initial buckling load decreases with increasing lordotic and kyphotic curvatures. When the body weight is taken into account as a load distributed along the whole spine, the calculated initial buckling load is twice the value that it is in the case of a single concentrated load acting at the top of the spine. Applying the large deflection theory, no relation is found between the increased slenderness of a spine and a ‘buckled’ configuration of a scoliotic spine