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I understand that there are several characteristics of curly hair which differ from straight hair (such as an asymmetrical distribution of disulphide bonds in curly hair), but really am struggling to understand the root cause of inherent curl on the macroscopic level.

My current understanding of the hair structure is based mostly upon this website

The most relevant part of the hair for our discussion is the cortex, which is made up of many axially aligned macrofibrils, or macroscopic keratin fibers, which are in some filler essentially of lipids/proteins. Inside these macrofibrils are microfibrils. These are also aligned axially and in some filler of lipids/ proteins. Inside the microfibrils are the protofibrils, even smaller fibers which are twisted around each other like a yarn. These protofibrils are made up of 4 keratin chains which are essentially twisted together and connected by disulphide bonds and hydrogen bonds. While hydrogen bonds are easily broken, the disulphide bonds are not. In curled hair, the macrofibril isn't symmetrical but I am unsure as to how this, or what other effects, actually lead to the curling.

I had previously assumed that the reason for curling is that in an asymmetrical configuration of the hair(IE not cylindrical but more oval in cross section), some residual stresses are formed by the disulphide bonds between the keratin, If this is true, it would lead me to believe that it would cause increased buckling of the protofibrils. But, even with straight hair and more symmetrical disulphide bonds, you already have some curling and buckling of the protofibrils, but the hair doesn't curl on a macroscopic level.

As such, it doesnt seem like this buckling due to asymetrical disulphide bonds would necessarily lead to a curled or organized structure on the macroscale, with the macrofibrils. This leads me to believe I am missing something.

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Nice question. I must say it took me many hours to get satisfactory answer.

Hairs are made of keratin molecules, which contain cysteine. Cysteine has thiol (-SH) group, by which it can form disulfide (-S-S-) bond with another cysteine of another keratin, causing bending of hair. See this image from here:

keratin molecules and disulfide bridges in hair

Curling of hair can be justified on both microscopic and macroscopic level.

  1. Microscopic level: See this post from here:

Curly hair has to do with the chemical bonds in the protein that makes up hair - $\alpha$-keratin. Keratins, particularly $\alpha$-keratin, have long sequences of amino acids (often more than 300) which forms a helical structure.

Pairs of these helical structures then coil about each other in a left-hand coiled-coil structure. These are then attracted to another coiled coil so two keratin helices will stick together. These four-chain structures then associates with another four-chain structure to form the hair filament. One of the amino acids which make up these chains, is cysteine which has a sulpher group which is able to make connections with other sulpher groups on other coiled coils.

The more interactions a filament has with another filament, the more tightly coiled the coiled-coil becomes. Hence, curly hair has more interactions than straight hair. The process of `perming' hair introduces more accessibility of the sulpher on the amino acid, cysteine, to make these connections. Finger and toe nails have many many bonds between filaments and are thus, very hard.

For example, see how hairs are curled artificially via perming.

bonding between keratin molecules

effect of disulfide bridges

Source

This change in location of bonds is what causes curling of the hair (look again at the first diagram and notice the orientation of disulfide bridges). Those vertical strands now get curled due to change in these bonds. Here, the required mechanical tension for bending is provided artificially.

  1. Macroscopic level: Shape of hairs is also determined by its macroscopic structure. Look at this article:

All hair, whether curly or straight, has two major components: the shaft and the follicle. The shafts are the visible, flowing strands that we see on our heads. The follicle is the part of our hair that resides within the skin, or dermis, of our scalp. Each of these structures plays a role in determining our overall hair shape.

Let’s start at the root of the issue (pun 100 percent intended): the follicle. It turns out that the shape of our follicles is a major determinant of our hair texture. If you were to look at the follicle of straight hair, you would find it is perfectly round. The follicle of curly hair adopts an oval shape. The flatter the oval is, the curlier the hair will be.

Another contributing factor to a hair’s curl is the way the follicle tunnels into the scalp. Follicles of straight hair tunnel vertically down from the skin’s surface into the dermis. If the follicle angles into the dermis then the hair will curve as it grows causing it curl. Although, this curving of the follicle can lead to gorgeous curls it causes one major drawback that all curly-haired persons can attest to, dryness. Within the dermis, special glands line the follicle to secrete oil, called sebum, to lubricate the hair. Unfortunately, when follicles curve sebum isn’t able to travel the length of the hair as well leading to dryness of hair that doesn’t get lubricated.

hair structurefollicle shapes and sizeseffect of follicle tunneling into scalpSource

Although how shape of follicle determines structure of hair strand is probably not known, the major contributing factor likely is how hair emerges from the scalp. When it emerges in a bent shape, it faces a lot of tension from the scalp, which causes it to bend in the shape of the follicle to form curls. Since straight-emerging strands don't face such forces, they do not lead to curled hairs.

In this way, hair curls are a consequence of large number of disulfide bridges between keratin molecules and how the hair emerges from the scalp.

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  • $\begingroup$ Yes, this is an excellent summary of essentially what I had read on the internet as well. However, it fails to fully address the root of the question: why exactly does the disulfide style bonding. We have two obvious contributors to curling: 1) high twisting in the alpha-keratin and 2) asymmetry in the cross section. It seems like 1) may change the elastic modulus of the hair, thus making it more susceptible to bending, while 2) changes the cross section and (assuming the cross sectional area is roughly the same) render the hair more vulnerable to curling. $\endgroup$
    – User2341
    Commented Sep 18, 2017 at 14:39
  • $\begingroup$ However, the root cause is still not addressed. There is some cause that is leading to the actual curling. The two factors mentioned previously don't directly cause curling, there must be some residual stress that occurs during the hair growing process. In my mind, this residual stress may occur in several different manners but most likely due to a change in surface chemistry as the hair grows into atmosphere. This change in surface chemistry likely leads to a change in mechanical properties, which in turn induces a mechanical stress and leads to curling. $\endgroup$
    – User2341
    Commented Sep 18, 2017 at 14:44
  • $\begingroup$ @user2341 it seems I still have not caught the root of the problem. Apologies, but could you please explain what I have failed to answr here? $\endgroup$ Commented Oct 6, 2017 at 5:41
  • $\begingroup$ As in my previous comment, there is no information regarding the cause of the curling. I went on to speculate as to causes in my previous comment, but I'm not sure that any actual evidence as to the cause or the reason why hair curls. $\endgroup$
    – User2341
    Commented Oct 6, 2017 at 21:35

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