Variance-mean analysis: A simple and reliable approach for investigating synaptic transmission and modulation

The mechanisms underlying synaptic plasticity can be investigated by analyzing synaptic amplitude fluctuations before and after a synaptic modulation. However, many older fluctuation analysis techniques rely on models of synaptic transmission that incorporate unrealistic simplifying assumptions or have too many free parameters. As a result, these techniques have sometimes produced counterintuitive or contradictory results. In contrast, the variance-mean (V-M) technique requires fewer assumptions and is more robust than previous approaches. It achieves these improvements by focusing on two key parameters of synaptic transmission, the average probability that a vesicle is released from a synaptic terminal following a presynaptic stimulus (P _av), and the average amplitude of the postsynaptic response to a vesicle of transmitter (Q_av). To apply V-M analysis, a fluctuating postsynaptic current (PSC) is recorded at several different extracellular Ca²⁺ or Cd²⁺ concentrations. The variance of the PSC amplitude is plotted against the mean amplitude at each concentration, forming a parabola. The degree of parabolic curvature estimates P_av, and the limiting slope under low release conditions estimates Q_av. The shape of the V-M parabola changes in characteristic ways following each of the three standard forms of synaptic modulation: a change in Q_av (postsynaptic), a change in P_av (presynaptic), or a change in the number of terminals (N). The approach does not require specialized software, and can even be implemented as a purely graphical technique. V-M analysis has been used to investigate the site of expression of long-term potentiation and the mechanisms underlying paired-pulse depression. This report presents a detailed mathematical development of the technique, and explores the limiting conditions under which it can confidently be applied. V-M analysis requires fewer than 100 PSC amplitude measurements to accurately estimate P_av and Q_av, and it can reliably identify whether a synaptic modulation occurs at a pre- or postsynaptic site. In contrast to other techniques, V-M analysis is largely insensitive to recording noise, nonuniform modulation and intrinsic variability of the unitary synaptic amplitude.