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

J Neurosci Methods. 2003 Dec 15;130(2):115-25. doi: 10.1016/j.jneumeth.2003.09.019.


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 (Pav), and the average amplitude of the postsynaptic response to a vesicle of transmitter (Qav). 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 Pav, and the limiting slope under low release conditions estimates Qav. The shape of the V-M parabola changes in characteristic ways following each of the three standard forms of synaptic modulation: a change in Qav (postsynaptic), a change in Pav (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 Pav and Qav, 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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Analysis of Variance
  • Animals
  • Cadmium / metabolism
  • Cadmium / pharmacology
  • Calcium / metabolism
  • Calcium / pharmacology
  • Dentate Gyrus / cytology
  • Dentate Gyrus / physiology
  • Extracellular Fluid / drug effects
  • Extracellular Fluid / metabolism
  • Long-Term Potentiation / physiology
  • Models, Neurological*
  • Models, Statistical
  • Neuronal Plasticity / physiology*
  • Presynaptic Terminals / drug effects
  • Presynaptic Terminals / physiology*
  • Reproducibility of Results
  • Signal Processing, Computer-Assisted
  • Synaptic Membranes / drug effects
  • Synaptic Membranes / physiology
  • Synaptic Transmission / drug effects
  • Synaptic Transmission / physiology*
  • Synaptic Vesicles / drug effects
  • Synaptic Vesicles / physiology*


  • Cadmium
  • Calcium