Johnson-Nyquist noise
Johnson-Nyquist (thermal) noise is the voltage noise generated by the random thermal motion of charge carriers in any resistive element, and it sets a floor on how quietly an electrode can record. Its mean-square voltage is 4 kT R B (k Boltzmann's constant, T absolute temperature, R the resistance, B the bandwidth), so noise scales with the square root of resistance and of bandwidth. For an electrode the relevant resistance is the real part of the interface impedance, which is why high-impedance microelectrodes are intrinsically noisier and why lowering impedance with coatings improves the noise floor.
Thermal noise is white (flat across frequency), but real electrodes also show excess low-frequency 1/f (flicker) noise from interfacial electrochemistry, so the total electrode noise is a thermal floor plus a 1/f rise at low frequencies. In practice the recorded noise combines electrode thermal noise, this 1/f component, amplifier input-referred noise, and biological background activity; distinguishing them matters because only some can be reduced by electrode engineering, and averaging improves signal-to-noise only as the square root of the number of trials against the uncorrelated part.
Quoting only a 1 kHz impedance implies a thermal-noise estimate but omits the 1/f component and amplifier noise; the measured noise floor is often higher than the thermal prediction, especially at low frequencies.