A diffusion-activation model of CaMKII translocation waves in dendrites

Abstract

Ca2+-calmodulin-dependent protein kinase II (CaMKII) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed that stimulating dendrites locally with a single glutamate/glycine puff induces a local translocation of CaMKII into spines that subsequently spreads in a wave-like manner towards the distal dendritic arbor. Here we present a mathematical model of the diffusion, activation and translocation of dendritic CaMKII. We show how the nonlinear dynamics of CaMKII diffusion-activation generates a propagating translocation wave, provided that the rate of activation is sufficiently fast. We also derive an explicit formula for the wave speed as a function of physiological parameters such as the diffusivity of CaMKII and the density of spines. Our model provides a quantitative framework for understanding the spread of CaMKII translocation and its possible role in heterosynaptic plasticity.

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

“…New experimental findings in calcium transport and reaction transport in neuroscience [10] (see also [11]) open new questions on the geometric impact on the calcium transport in spiny dendrites and extension of a general scheme of this description of reaction under subdiffusion. An important new trend here is investigation of the influence of dendrite geometry on the reaction transport characteristics.…”

Propagation of CaMKII translocation waves in heterogeneous spiny dendrites

“…Our previous mathematical model of CaMKII translocation waves within a dendrite (Earnshaw and Bressloff 2010) is based upon an experimentally motivated mechanism proposed by Rose et al (2009), which is illustrated in Fig. 2.…”

“…The model is given by a system of reaction-diffusion equations for the concentrations of activated and primed CaMKII along a uniform one-dimensional non-branching dendritic cable. These equations incorporate three major components of the dynamics: diffusion of CaMKII along the dendrite, activation of primed CaMKII, and translocation of activated CaMKII from the dendrite to spines (Earnshaw and Bressloff 2010):…”

“…(2.1) and (2.2) and linearizing near the leading edge of the wave where P → P 0 and A → 0. Requiring that the solution remains positive within the leading edge then shows that a traveling wave solution with speed c only exists if (Earnshaw and Bressloff 2010) …”

“…In Sect. 2, we briefly describe our previous model of translocation waves (Earnshaw and Bressloff 2010) and summarize some of the predictions of the model. In Sect.…”