Table 1.

Glossary of symbols and acronyms

Symbol	Meaning	Notes
Measurable extra-cellular quantities
ø(t)	running direction
s(t)	running speed
ν(t)	running velocity
G	spatial scale of the grid	Distance between adjacent firing fields.
fi(t)	intrinsic firing frequency	Estimated from spike-train autocorrelogram. Assumed to reflect neuron’s MPO frequency.
fθ(t)	theta frequency	Measured from the extra-cellular EEG. Assumed to vary with running speed.
f0	theta frequency extrapolated to zero running speed	Intercept of the plot of theta freq. fθ(t) (or intrinsic freq. fi(t)) versus running speed s(t).
Symbols and acronyms describing the model
MPO	membrane potential oscillation
VCO	velocity-controlled oscillator	MPO whose frequency (fa) increases with depolarization by a velocity-dependent synaptic input.
d, ød	‘preferred’ direction	Running direction producing the VCO’s maximum frequency. Shown as a unit vector d or angle ød as convenient.
fb(t)	‘baseline’ frequency
fa(t)	‘active’ frequency	Frequency of VCO: fa(t) = fb(t)+βv(t).d.
β	free parameter	The gain of the VCO response to depolarization. Spatial scale G=2/√3β.
T	time constant for leaky integration of grid cell inputs	T and F set so that roughly coincident inputs from ≥2 VCOs are required for firing.
F	firing threshold on grid cell MPO