Propagation of CaMKII translocation waves in heterogeneous spiny dendrites

Abstract

CaMKII (Ca 2+ -calmodulin-dependent protein kinase II) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed experimentally that stimulating a local region of dendrite not only induces the local translocation of CaMKII from the dendritic shaft to synaptic targets within spines, but also initiates a wave of CaMKII translocation that spreads distally through the dendrite with an average speed of order 1µm/s. We have previously developed a simple reaction-diffusion model of CaMKII translocation waves that can account for the observed wavespeed and predicts wave propagation failure if the density of spines is too high. A major simplification of our previous model was to treat the distribution of spines as spatially uniform. However, there are at least two sources of heterogeneity in the spine distribution that occur on two different spatial scales. First, spines are discrete entities that are joined to a dendritic branch via a thin spine neck of submicron radius, resulting in spatial variations in spine density at the micron level. The second source of heterogeneity occurs on a much longer length scale and reflects the experimental observation that there is a slow proximal to distal variation in the density of spines. In this paper, we analyze how both sources of heterogeneity modulate the speed of CaMKII translocation waves along a spiny dendrite. We adapt methods from the study of the spread of biological invasions in heterogeneous environments, including homogenization theory of pulsating fronts and Hamilton-Jacobi dynamics of sharp interfaces.

Cortical and Thalamic Interaction with Amygdala-to-Accumbens Synapses

“…Beyond biophysical summation, clustered synapses may also biochemically influence each other through the cytosol. The discrete structure of spines provides a relatively confined space that reduces the diffusion of spinal contents, but CaMKII and other plasticity-associated signaling proteins can "spill out" and propagate to adjacent spines when abundantly generated (Bressloff, 2013). As such, relatively low levels of signaling components resulting from weak activations, such as the activation induced by the 1 Hz pairing protocol, could be effectively confined within individual spines with limited spine-spine cross talk.…”

Aggregation–fragmentation model of vesicular transport in neurons

“…(2) Another simplification of our model is that it ignores the discrete and inhomogeneous nature of the distribution of synaptic targets-we simply treated the target concentration c as continuous and assumed vertical interactions between motors and targets. One method for handling the discrete nature of synaptic targets is homogenization theory, which we have previously used to analyze the diffusive transport of signaling molecules along spiny dendrites [31]. It should be possible to extend this approach to the more complex advection-diffusion model.…”

Reaction-subdiffusion front propagation in a comblike model of spiny dendrites

“…HereC[P (x,y,t)] ≡C(P ) is a reaction kinetic term. In particular, to model reaction kinetics inside dendrites, it can be considered either linear,C(P ) = CP , or logistic,C(P ) = CP (x,y,t)[1 − P (x,y,t)] [20]. Integration with the power law kernel t −γ ensures anomalous diffusion in both the dendrite and spines.…”

“…To study the translocation waves of CaMKII in spiny dendrites, a system of coupled reaction-diffusion equations was proposed [11], where reactions were considered inside dendrites between two chemicals and a Markovian switching with particles concentrated inside spines [11,17,20]. The failure of the propagation in terms of the switching rate has been observed numerically [11] as well.…”