12It is known that dendritic spines change their size and shape sponta-13 neously and sometimes to a large degree, but the function of this remains 14 unclear. Here, we quantify these changes using time-series analysis of con-15 focal data and demonstrate that spine size can follow different autoregres-16 sive integrated moving average (ARIMA) models and that shape-and size-17 changes are not correlated. We capture this behavior with a biophysical 18 model, based on the spines' actin dynamics, and find the presence of 1/f 19 noise. When investigating its origins, the model predicts that actin in the 20 dendritic spines self-organizes into a critical state, which creates a fine bal-21 ance between static actin filaments and free monomers. We speculate that 22 such a balance might be functionally beneficially to allow a spine to quickly 23 reconfigure itself after LTP induction. 24 25 Keywords: dendritic spines, actin, 1/f noise, self-organized 26 criticality, shape fluctuations, shape descriptors 27 * Corresponding Author and Lead Contact: mayte.bonilla-quintana@phys.uni-goettingen.deDendritic spines are small protrusions of dendrites where the postsynaptic part of 29 most excitatory synapses is located. It is well known that size and shape changes of 30 these spines are correlated with changes of the strength of excitatory synaptic con-31 nections (Matsuzaki et al., 2004). However, Fischer et al. (1998 observed that the 32 shape of dendritic spines also varies spontaneously during 30-minute recordings at 33 a 1.5-second frame-rate under basal conditions, under which spines are at the min-34 imum level of activity required to maintain their functions. Interestingly, nearly 35 all spines in these recordings survived and their volume and density stayed mostly 36 constant. Similar spine variations were measured by Dunaevsky et al. (1999) in 37 time-lapse images of acute and cultured slices from cerebellar Purkinje cells, and 38 cortical and hippocampal pyramidal cells. Rapid spine shape changes have also 39 been observed in living organotypic hippocampal mouse brain slices (Testa et al., 40 2012) and in the somatosensoty cortex of the adult mouse in vivo (Berning et al., 41 2012).
42Rapid changes of dendritic spine shapes are related to actin dynamics (Fischer 43 et al., 1998; Dunaevsky et al., 1999). Actin is a globular protein that assembles 44 into filaments, which are polar structures that continuously undergo a treadmilling 45 process. In this process, actin monomers are polymerized at the (+) end (barbed 46 end) of the actin filaments, while these filaments are depolymerized at the (-) end.
47Actin polymerization generates a force that moves the cell membrane forward 48 (Mogilner & Oster, 1996). Moreover, blockage of actin polymerization hinders 49 spine motility (Fischer et al., 1998; Dunaevsky et al., 1999). Honkura et al. (2008) 50 observed filamentous actin within a single spine and found that a dynamic pool of 51 actin, which has a fast treadmilling velocity and is mainly localized at the tip of 52 ...