That's a lot trickier of a problem, might make more sense for you to just convert the bindings to splines and then use a path deform modifier to spread a crinkled wire along the straight binding spline to fake it.
However, if you conjoin every nth sibling particle (where n > 1) together with a binding that has a shrunken length, you can achieve a crinkling effect. Luckily tyFlow's Particle Bind operator allows you to define sibling proximity, to add additional bindings every nth sibling particle.
Examine the attached file and you'll see I've added 2 additional sets of sibling particles (proximity 2 and 3 with an ID of 1) and used a Modify Bindings operator to shrink their length over time. As you'll see when you playback the animation the wire gets crinkled. If you go this route, remember when meshing the bindings with a Spline Paths operator, to filter by ID (0) or else the secondary crinkle bindings will get meshed as well.
However, if you conjoin every nth sibling particle (where n > 1) together with a binding that has a shrunken length, you can achieve a crinkling effect. Luckily tyFlow's Particle Bind operator allows you to define sibling proximity, to add additional bindings every nth sibling particle.
Examine the attached file and you'll see I've added 2 additional sets of sibling particles (proximity 2 and 3 with an ID of 1) and used a Modify Bindings operator to shrink their length over time. As you'll see when you playback the animation the wire gets crinkled. If you go this route, remember when meshing the bindings with a Spline Paths operator, to filter by ID (0) or else the secondary crinkle bindings will get meshed as well.