I. The Core Concept: Consistency of Angles

In neuroscience, phase locking mathematically means consistency of angles. You collect a sequence of phase angles (0° to 360°) and ask:

Are these angles random (uniform), or do they cluster around a specific direction?

However, the term is used in two very different experimental contexts depending on what is locking to what.

II. Type 1: Spike-Field Phase Locking (Internal Sync)

“Phase locking refers to the tendency of a neuron to fire action potentials at particular phases of an ongoing periodic sound waveform, such as the sinusoidal waveforms that are typically used in physiological studies of the auditory system”

— Encyclopedia of Neuroscience, 2009

  • Synonyms: Spike-field coherence , spike-phase coupling.
  • What is locking? A single neuron’s firing (spike train).
  • What is it locking to? An internal brain rhythm (LFP/Theta Wave).
  • The Reference Frame: The brain’s clock (the cycle of the wave itself).
  • The Question: “Does this neuron fire in sync with the background beat of the hippocampus?”

Mechanism: The LFP oscillation acts as a “conductor.” When the voltage is at a specific phase (e.g., the trough), the membrane potential of the neuron is pushed closer to threshold, making it more likely to fire.

  • Result: Spikes cluster at the “preferred phase” of the oscillation.
  • Meaning: This proves Network Connectivity. It confirms the single neuron is physically “plugged in” to the local population dynamics.

III. Type 2: Inter-Trial Phase Locking (External Sync)

“Activity is phase-locked when its phase is the same or very similar on each trial”

— Cohen, M. X. Analyzing Neural Time Series Data: Theory and Practice, Chapter 3

Context: EEG/ERP Analysis (Cohen, Chapter 2). Synonyms: Inter-Trial Phase Clustering (ITPC), Phase-Locking Value (PLV).

  • What is locking? A macroscopic voltage wave (EEG/LFP).
  • What is it locking to? An External Event (Stimulus Onset / $t=0$).
  • The Reference Frame: The Experimenter’s Clock.
  • The Question: “Does the brain start oscillating with the exact same phase every time I show the picture?”

Mechanism: This distinction is used to separate Evoked from Induced activity.

  1. Phase-Locked (Evoked): The stimulus “resets” the phase of the oscillation. On Trial 1, 2, and 3, the wave starts with a peak at 100ms.
    • Result: Creates an ERP (Event-Related Potential).
  2. Non-Phase-Locked (Induced): The stimulus increases the power of the oscillation, but the phase is random. On Trial 1 it’s a peak; on Trial 2 it’s a trough.
    • Result: Invisible in ERPs (cancels out). Visible in Time-Frequency Power.

IV. Comparison: The Musician vs. The Sprinter

The best way to remember the difference is through analogy:

Feature Type 1: Spike-Field (Internal) Type 2: Inter-Trial (External)
The Analogy The Jazz Musician The Sprinter
Description A drummer who always hits the snare drum exactly on the 3rd beat of the song. A runner who always launches exactly 100ms after the starting gun fires.
Synchronization Syncs to the Rhythm (Continuous). Syncs to the Trigger (Discrete).
Data Source Correlation between Spikes and LFP. Correlation between Trial 1, Trial 2, Trial 3…
Scientific Value Validates Probe Location and Network Membership. Validates Stimulus Determinism and Evoked Potentials.

V. The Mathematical Unity

Despite the conceptual difference, the statistical test used is often identical (The Rayleigh Test).

  1. Extract Angles:
    • Type 1: Collect the LFP phase angle at every spike timestamp ($\phi_{spike}$).
    • Type 2: Collect the EEG phase angle at time $t$ across all trials ($\phi_{trial}$).
  2. Vector Sum: Treat each angle as a vector on a unit circle.
  3. Calculate Length:
    • If the vector length $\approx 0$, the activity is Random (Unlocked).
    • If the vector length $\approx 1$, the activity is Clustered (Locked).

Summary:

  • Spike-Field Locking tells you about the Brain’s Internal Wiring (Spike $\leftrightarrow$ Wave).
  • Inter-Trial Locking tells you about the Brain’s Reaction to the World (Stimulus $\leftrightarrow$ Wave).