Moving a line geometry with three.js using GLSL - three.js

Question

I have a line geometry made with three.js, which I want to move as a spermatozoid (i.e. the head moves first, then all of the points along the tail move accordingly to the head) using GLSL.
Here is a visual representation of what I want:
So as you can see, point G eases to (follows) H, which in turn follows point E, which in turn follows the head.
I have a working examples, being animated on the CPU. Here is the code:
class Boid {
constructor (position) {
this.position = position
this.speed = 0.0009 + Math.random() * 0.0003
this.pointsNum = 12
this.points = []
this.line = null
this.angle = Math.random() * 360
for (let i = 0; i < this.pointsNum; i += 1) {
this.points.push(new THREE.Vector3(1, 1, 1))
}
this.angle = 0
}
update (target, time) {
if (time) {
this.line.geometry.verticesNeedUpdate = true
this.line.geometry.vertices.forEach((p, i) => {
let nextP = this.line.geometry.vertices[i + 1]
if (nextP) {
// if it's not the HEAD point, follow the next point in the geometry vertices
p.x += (nextP.x - p.x) * (time * 8.0)
p.y += (nextP.y - p.y) * (time * 8.0)
p.z += (nextP.z - p.z) * (time * 8.0)
} else {
// if the point is in fact the head, ease it according to some random moving point in our scene (target)
p.x += (target.x - p.x) * time
p.y += (target.y - p.y) * time
p.z += (target.z - p.z) * time
}
})
}
}
}
And here is a working example.
This technique is working, but would like to accomplish the same stuff with GLSL. My question is how should I approach it? Should I pass the next vertex position to the previous one and ease in my vertex shader? How should I keep track of the next's point position?
Any help is more then appreciated, I have been thinking about this a lot without any success.