0. C(m)=∑n=0N−m−1(xn−1N∑i=0N−1xi)(x(n+m)−1N∑i=0N−1xi). Here, xn represents the spine SEP enrichment values at the nth spine, with N the number of spines for the dendrite, and m, the spine lag. The regression lines for spine enrichment values were used to examine distance-dependent changes. To determine the number of synapses in clusters that would produce the autocorrelation values we obtained, we performed simulations (depicted in Figure S6). The following procedure was conducted GDC-941 to generate dendrites with simulated enrichment values satisfying different cluster distributions. We considered a series of 40 spines per dendritic segment and assigned an initial enrichment value
to each spine that varied randomly from 0 to 1. On top of these values, a cluster of enrichment-potentiated spines was added. Two cluster parameters were varied: cluster size and potentiation value of enrichment. A cluster size was characterized by Gaussian-distributed enrichment potentiation values along a dendrite with SD σ = 0.8, 1.2, and 1.6. Enrichment Selleck Docetaxel potentiation p varied from 2 to 5.5. To simulate a dendrite with σ cluster size and potentiation factor p, a Gaussian distribution with
SD = σ and maximum value p was multiplied by a random number (between 0 and 1) at each spine lag and added at a random location within the initial 40 spine enrichment values. By calculating an autocorrelation coefficient for each dendrite and repeating the same procedure 10,000 times, we derived an average autocorrelation curve for each parameter combination. By fitting the true data with the simulated data, we determined σ and the potentiation factor p (i.e., the number of potentiated synapses) in the cluster. Simulations were carried out using MATLAB (MathWorks). We thank C. Cepko for pCALNL-DsRed (Addgene 13769) and pCAG-ERT2CreERT2 (Addgene 13777), W. Guo for cloning the DNA constructs, D. Bortone for technical advice, and J. Isaacson, T. Komiyama and M. Scanziani for critical comments on the manuscript. This study was supported by National Institutes of Health (to
R.M.) and Elizabeth-Sloan Livingston Fellowship (to H.M.). Cell press “
“During brain development neurons establish highly specific synaptic connections with each other. This process is not only regulated by molecular factors that determine, for example, the formation of connections in specific laminae of brain structures, but also by synaptic activity itself (Cline, 2003, Goodman and Shatz, 1993 and Sanes and Yamagata, 2009). In particular, the fine tuning of synaptic connectivity relies on activity-dependent mechanisms that require spontaneous activity that is generated in developing neuronal networks before an organism receives sensory inputs, as well as—later on—activity, which is evoked by sensory experience (Hua and Smith, 2004, Huberman et al., 2008 and Katz and Shatz, 1996).