Particular : animating the inside streaks of light streak

I'm not sure how you created the movement in the emitter. When you need help with any layer or effect you should select the layer, press the U key twice to reveal all of the properties you modified in the layer, and then embed the whole screenshot in the forum so we have some idea of your workflow. 

Baring a detailed workflow description I can only assume that you probably used a light as an emitter. If you want the position of the particles to change over time then you need to change some of the physics properties. If you want to create some kind of random motion in the emitter so the particle streams wrap around each other then you need to animate the rotation or size or direction of the emitter. 

This screenshot shows everything I did to create a climbing spiral of particles. Set a spotlight as an emitter, parented the spotlight to a null that rotates and moves up, animated z distance of the spotlight from the null, then modified the Emitter Properties and changed the life of the particles so they would not die. 

Show me a screenshot that shows how you created the particles in your comp and I can give you some on other controls you might want to experiment with. You may just need to animate the rotation of the emitter. 

Try introducing some turbulence. Without something happening to the physics