[Verse 1] Dorsal edge ticking fast, HCN channels stacked up dense, Ventral pole dragging slow, current leaking through the fence. Giocomo oh-seven mapped the slope along the axis line, Membrane time constant climbing, tau stretching out with time. Subthreshold oscillation drops in frequency as you glide, Resonance peak sliding downward, Garden oh-eight verified. Every neuron's got a rhythm, a clock inside its skin, Dorsal ticks like a metronome, ventral hums low and thin. [Chorus] Gradiente, gradiente, de dorsal a ventral, El canal HCN marca el compás natural. Rápido arriba, lento abajo, así funciona el mapa, Frecuencia cambia, la escala también se destapa. (Tau, frecuencia, resonancia — todo en cascada) [Verse 2] Knock out HCN1, watch the story flip and bend, Giocomo eleven, twenty-eleven, showed us where it lands — Grid fields stretch out wider, spacing grows without the brake, Fast conductance gone, the module makes a bigger stake. No channel means no clamp on how long depolarized can stay, Slower dynamics, wider hexagons across the tray. The knockout mouse writes proof in patterns on the floor, Intrinsic tuning sculpts the scale — that's what the data's for. [Chorus] Gradiente, gradiente, de dorsal a ventral, El canal HCN marca el compás natural. Rápido arriba, lento abajo, así funciona el mapa, Frecuencia cambia, la escala también se destapa. [Verse 3] Two theories reading one same slope, both listening to the beat — Oscillatory interference says frequency writes the sheet, Two waves that beat together, their difference draws the grid, Slower dorsal frequency means a smaller field, no lie it did. CAN network disagrees on wiring but agrees on scale, Time constant sets the gain on how far the bump can sail — Longer tau, slower decay, the activity glides on, Integrates velocity longer, pushes farther before it's gone. [Bridge] Picture the bump of activity drifting on its bank, Now stretch the membrane's tau — watch it drift beyond the plank. Slower decay means the network holds the signal past its due, Velocity input keeps steering while the trace is still in view. So the bump travels farther for the same old step you take, Larger spacing between fields, a bigger scale to make. Short tau clamps it tight, keeps the module compact and neat, Long tau loosens the leash — grid spacing can't compete. [Chorus] Gradiente, gradiente, de dorsal a ventral, El canal HCN marca el compás natural. Rápido arriba, lento abajo, así funciona el mapa, Frecuencia cambia, la escala también se destapa. Tau más largo, ganancia más grande, así se destapa. [Outro] Dorsal fast, ventral slow, the axis writes the score, HCN, tau, and rhythm — the gradient's at the core. Knock it out, the scale expands, the story stays the same: Intrinsic properties, mapa vivo, spelling out the brain.
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