I don't know if the two processes are the same (as discussed in the previous posts), or if maturation of the body parallels the changes in the soul, because the keili must be able to receive the oir, but here are some of the changes that happen with a few kinds of inhibitory neurons (source). If you're not interested in Neuroscience, you can skip to Chassidus after the figure.
(click on the image to enlarge)
Meanwhile, a quote from a ma'amor by Frierdiker Rebbe (Ma'amor 38 from the Chassidic Discourses translated to English, starting with: "Rabbi Yehoshua ben Levi said: Each and every day, a Heavenly voice goes forth..."):
The bodies of all created beings are physical, while their souls are spiritual. Though there are differences between the bodies and souls of each of the four categories of terrestrial beings — inanimate, vegetative, animal and man — there are also similarities. The physical bodies of inanimate objects conform to their souls, just as the physical substance of vegetation dovetails with its soul. So too, animal bodies suit their souls and human bodies correspond with their souls.
In all instances, the life-force which emanates from the soul causes the body itself to be alive (rather than there being a living soul in a dead body). Indeed, a body's physical life is completely dependent on the soul that vivifies it; bodies themselves can neither hear, see, nor understand. Nevertheless, the soul clothes itself in its body in such a fashion that the whole body lives withing each of its limbs. Thus, the eyes see, the hands work. Unlike a machine which moves in response to an external activating force, the body enjoys an internal G-dly unity with its soul (and is thus itself alive). This causes both body and soul to feel the purpose for which G-d created them, and to fulfill G-d's desire by implementing their role in creation.
Just as G-d's desire for body and soul to unite causes the physical body to conform precisely to the soul that enlivens it, so too does the soul conform with the physical body, so that it is able to imbue all of with life. Thus, the unification of the spiritual soul with the corporeal body causes body to attain a loftier status than it had enjoyed previously.
Conversely, that part of the spiritual soul which permeates the body is, upon its descent, lowered in spiritual status. Previously it was a wholly spiritual being, with no connection to physicality, and was included within the hierarchy of the spirit.
The Midrash states that the soul is divided into five distinct categories: Nefesh, Ruach, Neshamah, Chaya and Yechidah. Each name indicates an aspect of the soul's function. The highest part is Yechidah and the lowest is Nefesh, whose purpose is to enliven the body. All five parts are connected, and before G-d sends a soul down to animate a body, Nefesh (the part that actually descends) is integrated with the other four soul levels. [...]The Frierdiker Rebbe goes on to say that even after its descent, Nefesh is still connected with the other parts of the soul, albeit less consciously or fully. As a result, Nefesh is capable of sensing, for instance, the Heavenly voice (heard by Chaya) which daily urges Yidden to repent and do mitzvos. This sensation is what drives many Jews to do something positive and constructive in their lives, although for many of them, that urge is misdirected. (It is also the reason why sometimes we get sudden bursts of energy and inspiration, both in our material affairs and in the different aspects of avoida, such as learning or davening.)
Nefesh is also able to express Yechida when a Jew goes on mesirus nefesh, chv"sh, or when he meditates on how he is capable on going on mesirus nefesh not to separate himself from Hashem and how each sin separates him from Hashem due to being a micro-act of avoida zarah. As a result of this meditation, the Jew's hidden love is aroused, and he does not sin.